Several models are used in this study, all of which include prognostic dust. The atmospheric component of an Earth system model, the Community Atmospheric Model (CAM4) of the Community Earth System Model (CESM) (Neale et al., 2013; Hurrell et al., 2013) is capable being forced either by online-calculated dynamical winds or by reanalysis datasets and is the model used for the bulk of the analysis to test sensitivity to which reanalysis winds are used (Sects. 2.1.1 and 2.1.2). To contrast with this model, results from other models, including the CAM5 version of the same model, and two chemical transport models, driven by reanalyses, are also used (Model of Atmospheric Transport and Chemistry, or MATCH, and GEOS-chem) (Sect. 2.1.3). More details are described below, along with a summary of the model simulations (Table 1).

For completeness, we compare standard annual means from each simulation to available data (e.g., Ginoux et al., 2001; Huneeus et al., 2011) in order to show that the mean dust cycle is reasonable in our models. In this study, we use the annual-mean surface concentration, AOD and deposition compilations from Albani et al. (2014).

For the variability studies, data were chosen for overlap with model runs and availability of longer datasets to evaluate interannual variability. In situ observations from the University of Miami network (Prospero and Nees, 1986; Prospero et al., 1996; Arimoto et al., 1990, 1997) were used here, as compiled in Luo et al. (2003) and Mahowald et al. (2003) and updated at some sites (Prospero and Lamb, 2003). In addition, in situ observations from three sites in northern Africa from the AMMA (African Monsoon Multidisciplinary Analysis) campaign were included (Marticorena et al., 2010). Details on the individual sites and locations are included in Table 2, and are shown in Figs. S1, S3 and S5 in the Supplement.

Sun-photometer-derived AOD is included from the AERONET (Aerosol Robotic Network) database (Holben et al., 1998). Only sites where more than 50 % of the modeled AOD was from dust are included in this comparison (as filtered in Fig. 1 using in Mahowald et al., 2007), and only sites with more than 18 months of data are used here to estimate variability (Table 2). Because both sea salt and dust occur in the coarse mode, we cannot use remote sensing measurements of the coarse vs. fine mode to identify dust-dominated stations.

Two sites in the Southern Hemisphere are included (bottom of Table 2): surface concentration data from Rio Gallegos (Zihan, 2016) and deposition data from Kerguelen (Heimburger et al., 2012). Because of the limited datasets in the Southern Hemisphere, we will consider these sites separately in Sect. 3.3. Although there are no AERONET data using these Northern Hemisphere criteria available in the Southern Hemisphere, if we focus on the coarse mode, there is one station which is dominated by dust (i.e., far from the coasts, where sea salts would make up a large percentage of the total aerosol load): Tinga Tingana in southeastern Australia. Located in a region of predominately westerly winds, Tinga Tingana lies downwind of the central Australian desert, allowing desert dust to feature prominently in its aerosol load. Tinga Tingana also has a data record beginning in September of 2002, which overlaps our chosen time period by more than 3 years, making this the best Southern Hemisphere site to evaluate our modeled AOD variability.

For evaluation of the models' precipitation, we use the CPC Merged Analysis of Precipitation (CMAP) (http://www.esrl.noaa.gov/psd/data/gridded/data.cmap.html) (Xie and Arkin, 1997). This is a combination of in situ and satellite observations, as well as models, to present the best estimate of precipitation.

For comparison of the variability in the modeled and observational values, we define variability similarly to previous studies (Mahowald et al., 2003): Variability=σμ, where σ is the standard deviation of the modeled and observed values, and μ is the mean.

Here, we focus on IAV, so that the annual means are used in Eq. (1) for that calculation. However, in order to contrast with the variability in the seasonal cycle, we will also report the strength of the seasonal cycle in terms of variability, where the values included are the climatological monthly means.

Models and observational time series of in situ concentrations and AOD (Table 2) were also correlated, using rank correlations to assess the ability of the models to simulate variability (similar to Mahowald et al., 2003). Rank correlations are used in order to reduce the importance of individual, extremely high data points, which can dominate regular correlations (Wilks, 2006). Similar to the variability, most of the analysis in the paper focuses on of the annual means, which test the ability of the models to simulate interannual variability, but some information about seasonal correlation is also provided, in order to provide context and comparison to previous studies.

We also analyze the observations and model output for trends, by calculating the least-squares fit slope, as well as the standard deviation in the slope.

In order to understand how similar model results are, we also calculate the variability at each grid box and compare different models at both the interannual and seasonal timescale. We also correlate the time series of models at individual grid boxes across model simulations, again on the two different timescales.

To show the sensitivity to meteorology, we correlate the three CAM4 reanalysis simulations (CAM4-RE) which will give us three different correlation coefficients (CAM4-MERRA vs. CAM4-NCEP; CAM4-MERRA vs. CAM4-ERAI; and CAM4-NCEP vs. CAM4-ERAI) and then average at each grid point the three different correlation coefficients to find the average correlation. Similar results are conducted using the AMIP simulations (CAM4-AMIP vs. CAM5-AMIP), and for the model simulations using the exact same meteorology (CAM4-MERRA vs. GCHEM-MERRA and CAM4-NCEP vs. MATCH-NCEP).

Finally, we use the model values to estimate the number of monthly mean observations required to correctly estimate the climatological annual mean value over 1990–2005. To do this, we assume that we would like to have a 95 % chance to be within 1 standard deviation of the climatological mean. 1000 Monte Carlo simulations were conducted, and each time we chose randomly from the modeled monthly mean values at each grid point, and for each number of observations (between 1 and 50) we calculated the percentage of the time that the mean is within 1 standard deviation of the climatological mean of the 1990–2005 simulation. At every grid box, the number of observations that would meet the 95 % criteria is then calculated, providing an estimate of the number of months of observations required.

Note that the modeled monthly mean values are not at all Gaussian distributed, and thus normal methods for determining the number of observations would not work (e.g., Wilks, 2006). Thus, for this analysis, we use rank correlations, which work with non-gaussian data. To be consistent with the climate model community (Taylor, 2001; Gleckler et al., 2008), for mean and standard deviation analysis described above, we use these standard metrics, despite the fact that our datasets do have not Gaussian distribution, which will lead to some errors in our results.

The annual mean distribution of the model simulations included here are evaluated elsewhere in more detail, since many of these model results were previously published (Luo et al., 2003; Huneeus et al., 2011; Albani et al., 2014; Ridley et al., 2013, 2014), but for completeness we repeat comparisons of annual mean surface concentration, AOD and deposition between available observations and the model simulations in the online Supplement (Table S3; Figs. S1–S6). Concentrations vary over several orders of magnitude spatially, and the models are able to simulate these variations (Figs. S1 and S2). In addition, the models can be shown to be mostly accurate in simulating the observed dust AOD and deposition (Figs. S3–S6). Most of the model versions presented here do an equally good job when compared against the observations (Table 3). Note that the CAM4 and CAM5 simulations were tuned against these same observations (Albani et al., 2014), while the MATCH (NCEP) and GCHEM (MERRA) models were previously compared to similar observational syntheses (Luo et al., 2003; Huneeus et al., 2011; Ridley et al., 2013, 2014).

The mean source flux and globally averaged AOD of the three CAM4-RE are 2400 ± 26 % Tg yr-1 and 0.026 ± 30 %, respectively, while for all the models included here the mean emission flux and AOD are 2400 ± 26 and 0.025 ± 40 %, respectively. These ranges are similar to previous studies (Huneeus et al., 2011; Reddy et al., 2005). Note that using a similar model (CAM4-RE) and similar methodology to constrain the dust AOD, based on a combination of surface concentration, deposition and AOD in dust regions (Albani et al., 2014) obtains an uncertainty just due to meteorology of 30 %. A more recent estimate, based more extensively on remote sensing data with limited information from four different models, but without using deposition or surface concentration data, finds a higher AOD of 0.033 ± 0.006 than found here, and a much smaller error estimate (Ridley et al., 2016). Thus there are large differences in the deduced AOD and uncertainties depending on assumptions about how to include different data, as well as the details of the models and methodology used.

Since this study is focused on an inter-comparison of different model simulations, rather than an evaluation of a specific model, we conduct limited comparison to observations. We focus on the highest quality data, coming from in situ concentrations and sun photometry data in dust-dominated regions (e.g., Prospero and Lamb, 2003; Holben et al., 1998; Table 2), and ignore satellite-based measurements (e.g., Torres et al., 2002; Evan et al., 2006) and dust visibility data (Mahowald et al., 2007) which are more difficult to interpret, both because they are not always only dust aerosols, and because they can have larger errors and thus be more difficult to compare for interannual variability (Torres et al., 2002; Evan et al., 2006; Mahowald et al., 2007). Some previous studies have included comparison of these in situ and sun photometry data in terms of interannual variability for specific model simulation evaluation (e.g., Mahowald et al., 2003; Ridley et al., 2014). The vertical distribution of the aerosol can also vary depending on the meteorology used (e.g., Albani et al., 2014), which may introduce some additional variability and discrepancy for in situ ground-based measurements.

Focusing on the amount of IAV, the models tend to simulate values between 0.1 and 0.8 for the variability (standard deviation of annual means divided by climatological annual mean; Sect. 2.3) at the observing sites, with largest values found at Mace Head in the models, but Bermuda in the observations. The models tend to simulate more IAV in AOD than in concentration (Fig. 1 vs. Fig. 2; Fig. 3a vs. Fig. 3b), while the observations suggest similar amounts of variability (Fig. 1 vs. Fig. 2; Fig. 3a vs. Fig. 3b). Both the models and the observations suggest much more variability (> 2-fold) in the seasonal cycle than in the IAV (contrast Fig. 1 vs. Fig. S7 or Fig. 2 vs. Fig. S8; Table S1 vs. Table S2 in the Supplement; or Fig. 3c and d) at many sites (Banizoumbou, Barbados, Bermuda, Zinzana, Miami, Midway, Dalandzadgad and Sedé Boqer), and only slightly larger (1–2-fold) at the other sites.

Next we evaluate the ability of the models to simulate the high and low annual means using rank correlations. Most of the models do not have statistically significant correlation coefficients (Fig. 3e and f; Table S3). The models do much worse at simulating IAV than the seasonal cycle (contrast Figs. 1 and 2 with Figs. S7 and S8; Fig. 3e and f with Fig. 3g and h), since at most stations, the models have a statistically significant correlation for the seasonal cycle and simulate a similar amount of variability over the seasonal cycle. For the seasonal cycle, the exceptions are at Izaña and Ilorin for all of the models, and the CAM4 (AMIP) simulation, which is not statistically significantly correlated at most of the stations (Table S3; Fig. 3e and f). For the CAM4, forcing with only sea surface temperatures (SSTs) substantially degrades the ability of the dust model to simulate the seasonal cycle, while in CAM5, the seasonal cycle is better simulated.

In model intercomparisons it has been observed that the model mean often does a better job than the individual model simulations (e.g., Flato et al., 2013). We evaluate this in the case of dust using the average of the CAM4 reanalysis models – CAM4 (MERRA), CAM4 (NCEP) and CAM4 (ERAI). At the observational sites considered here, we do not see a large increase in the correlation coefficients for the model average vs. individual models for either the IAV (Table S3) or the seasonal cycle (Table S4).

Overall this section supports previous studies (Prospero, 1996; Mahowald et al., 2003; Ginoux et al., 2004; Marticorena et al., 2010), suggesting that at the limited observational stations (Table 2) located mostly in the Northern Hemisphere (Fig. 2e), seasonal variability is larger than interannual variability (Tables S2 and S3; Fig. 3c and d), and that the model can simulate seasonal variability better than interannual variability in both surface concentrations and AOD (Fig. 1 vs. Fig. S7; Fig. 2 vs. Fig. S8; Fig. 3e vs. Fig. 3g; and Fig. 3f vs. Fig. 3h). Taken overall, the models driven by reanalysis winds – all except CAM4 (AMIP) and CAM5 (AMIP) – compare roughly similarly against the available observations for both seasonal cycle and interannual variability (Fig. 3).

New in this section is the evaluation of the relative ability of reanalysis-driven models vs. sea surface temperature forced models – CAM4 reanalysis vs. CAM4 (AMIP) – which suggests a degradation in the ability of the models driven only by sea surface temperature to simulate both seasonal and interannual variability, although this is dependent on which model version (CAM4 vs. CAM5; Tables S3 and S4; Fig. 3). This correlation potentially provides insight into how much of the variability in dust is driven by sea surface temperatures. There are also significant differences between models driven by the same meteorology (e.g., CAM4 (MERRA) vs. GCHEM (MERRA) and CAM4 (NCEP) and MATCH (NCEP), highlighting the importance of model formulation as well as meteorology. We will return to these points in later sections.

Recent studies have highlighted the importance of fluctuations in rainfall in the Sahel for driving interannual variability and decadal scale variability in North Atlantic dust concentrations as seen in Barbados (e.g., Prospero and Lamb, 2003), although the importance of land use, winds, surface roughness and vegetation changes have been noted as well (e.g., Marticorena and Bergametti, 1996; M'bourou et al., 1997; Mahowald et al., 2002, 2007; Cowie et al., 2013). Since 2000, it has been noted that the Sahel precipitation no longer anti-correlates with dust at Barbados, suggesting a different mechanism may have become important. (Prospero, 2006; Mahowald et al., 2009). Ridley et al. (2014) proposes the hypothesis that the observed decrease in dust from 1982 to 2008 at Barbados is controlled by source wind strength over source regions in northern Africa. For this argument, they use model evaluation with the GCHEM (MERRA) model (a different version of which is also included here), as well as analysis of ERAI and NCEP reanalysis winds and other observations (Ridley et al., 2014). Indeed, station data in the northern African region, especially the Sahel, support the idea that winds decreased in this region between the late 1970s and 2003 (Mahowald et al., 2007), and there is also an observed widespread decrease in surface winds across many land regions (McVicar et al., 2012). Of course, there are many issues with the observation of surface winds due to small-scale effects of buildings or topography (e.g., discussed in McVicar et al., 2012), so it is unclear how robust trends in observed surface winds are. Note that data correlations between visibility and winds suggest that both precipitation (Prospero and Lamb, 2003) and winds (Engelstaedter and Washington, 2007) are important for changes in dust near the source regions of northern Africa (Mahowald et al., 2007). Importantly, Cowie et al. (2013) argue that the trends in surface winds and dust could be from changes in vegetation through the mechanism of surface roughness, which would also link these changes to precipitation. Note that because model-calculated surface roughness was not archived in the models, we cannot test the Cowie et al. (2013) hypothesis directly in this study.

Here we can consider whether the hypothesis put forward in Ridley et al. (2014), that the decrease in winds in the surface region is responsible for the observed annually averaged decrease in surface concentration at Barbados, is consistent with the simulated trends in the multiple models included in this analysis. For this part of the paper, we use the full time period of our models, although for some models only some of the 1982-2008 time period is available (Table 1). For simplicity we consider only annual averages. As shown in Ridley et al. (2014), there is a statistically significant downward trend in the data at Barbados (Table 4). All the model versions considered here simulate a downward trend in the data at Barbados, although for some models this is not a statistically significant trend – CAM4 (NCEP); CAM5 (AMIP). Only one model simulates the slope within 1 standard deviation of the observed value: the CAM4 (MERRA) (Table 4). The GCHEM (MERRA) overpredicts the magnitude of the negative slope as shown by Ridley et al. (2014), while the other model versions underpredict the magnitude of the slope (Table 4).

Only some of the models see a statistically significant decrease in source strength in northern Africa (Table 4), and some models predict an increase over this time period. However, a look at the trends in surface concentration across the models show that all the models see a decrease in surface concentrations that extends from the Sahel area of northern Africa across the tropical North Atlantic to Barbados (Fig. 4), supporting the idea that the source strength is decreased over the time period 1990–2005. While individual models might simulate downward or upward trends elsewhere, this is the only region that sees a consistent model signal across this time period (Fig. 4). If we focus on the Sahel (western) area of northern Africa, indeed, most of the models simulate a decrease in the source (Table 4); exceptions are CAM4 (ERAI) and CAM5 (AMIP). Since the visibility data in northern Africa also suggest a decrease across this time period in the western Sahel (Mahowald et al., 2007), these support the idea that the decrease in the source is the cause of the decrease in Barbados surface concentrations. In the CAM4 models, the strongest correlation in IAV of the source occurs with surface winds (Table S5), and indeed in all the models there is a decrease in surface winds over this time period over the source regions, as seen in Ridley et al. (2014) (Table S6).

There is also a correlation between Sahel precipitation and Barbados concentrations (Prospero and Lamb, 2003), or precipitation and visibility in the Sahel (e.g., Mbourou et al., 1997; Mahowald et al., 2007), so the other driver could be precipitation. In some of the CAM4 model simulations, the IAV of the source strength does feature significant correlations with both LAI and precipitation, but in general those same cases feature even stronger correlations with surface winds (Table S6). Although the quality of the surface wind data precludes us from evaluating the reanalysis for surface winds, as discussed in McVicar et al. (2012), we can evaluate the precipitation, which is commonly done (e.g., Trenberth and Guillemot, 1998). When we do, we see that the reanalysis precipitation datasets are not capturing either interannual variability in precipitation or the slope in the precipitation, compared to the CMAP precipitation compilation (more details in Sect. 2.2) (Table 4). Since precipitation and winds, perhaps due to gustiness in moist convection (Engelstaedter and Washington, 2007) or due to surface roughness changes from vegetation (Cowie et al., 2013), are likely related to each other, an error in the IAV of precipitation may be indicative of an error in the IAV of winds.

Overall, the model simulations conducted here support the hypothesis of Ridley et al. (2014), although the quality of the reanalysis data forcing our simulations does not allow us to be conclusive about our results.

Most of the available dust observations come from the Northern Hemisphere (Table 2). Here we consider three sets of data from the Southern Hemisphere, one of surface concentrations in Rio Gallegos (Argentina/Patagonia, 52∘ S, 69∘ W) (Zihan, 2016) and one of the deposition at Kerguelen Island (49∘ S, 70∘ E), which is likely to be influenced by both South American and South African dust sources (such as the Patagonian and Namib deserts; Heimburger et al., 2012; Fig. 5). Finally, there is one AERONET station with data in the coarse mode, which is likely to be dominated by dust, since it is far from the coast and downwind of the Australian desert (Tinga Tingana, 29∘ S, 140∘ E) (Fig. S9); Notice that there are very few data at the first two observational sites, which means these results need to be interpreted carefully, especially for IAV, since 1.5 years of data are measured (Fig. 5). The surface concentration data at Rio Gallegos suggest an IAV variability of 0.08 (Table 5), which is at the lower edge, but in the same range as the observations in the Northern Hemisphere (values between 0.06 and 0.4; Fig. 3a; Table S1). The models, however, tend to predict too large a variability at this site (between 0.2 and 2). It is unclear why the models overpredict the variability, but it may be due to issues with the actual location of the sources in the model compared to the observations, or the strength of the north–south gradient in concentrations in the models vs. observations (e.g., Gaiero, 2007; Gassó et al., 2010). In addition, the way the tuning in Albani et al. (2014) was conducted will increase the interannual variability of the dust cycle in the CAM4 and CAM5 simulations in the Southern Hemisphere (Table 5). These model simulations had too small an emission value from some regions and too large from others, and thus the model source strengths were tuned in order to broadly match observations (Albani et al., 2014). In particular, in Argentina, the dust-source strength had to be tuned up very strongly in order to obtain a climatological dust that matched observations. This means that there were very few grid boxes and time periods with active sources, increasing the temporal variability in the model. If we had instead changed the wind threshold in our model formulation in order to tune the source strength (e.g., Tegen and Miller, 1998), we presumably would not have increased our variability as much, highlighting the importance of details in the model formulation for model results. The CAM4-ERAI and CAM4-AMIP simulations especially overpredict variability. Note, however, that some of the CAM4 models (CAM4 (MERRA) and CAM4 (NCEP)) have similar variability as the non-CAM4 models (GCHEM (MERRA) and MATCH (NCEP)), especially at Kerguelen and Tinga Tingana, suggesting that some of this variability may also be associated with the meteorological dataset. We will explore the ramifications for variability predictions in Sects. 3.4 and 3.5. Further downstream of the sources, the amount of variability in deposition observed at Kerguelen is 0.10, which is overpredicted in most of the models (Table 5), while at Tinga Tingana, the IAV variability is 0.42 in the observations, and tends to be smaller in the models.

At both Rio Gallegos and Tinga Tingana, the ratio of the IAV variability to the seasonal variability is 1.4 and 1.5, which are on the lower side of the observations in the Northern Hemisphere (Fig. 3c and d; Table S1). The models are able to simulate the reduced fraction of variability due to the seasonal cycle at these sites (Table 5). Because of the limited data and length of data, we cannot be sure, but the observations presented here are consistent with a stronger role of interannual variability, compared to seasonal variability, in dust sources in the Southern Hemisphere than in the Northern Hemisphere, as simulated by the models. Additional long-term data in the Southern Hemisphere would allow more testing of this model result.

Consistent with previous studies (e.g., Tegen and Miller, 1998; Mahowald et al., 2003, 2011), the largest variability in IAV (standard deviation over the mean, described in Eq. 1, Sect. 2.3) in modeled dust concentrations occurs not in the main dust-source areas or outflow regions of the North Atlantic, but rather adjacent to these regions, where intermittent dust events occur (Fig. 6a)(for example, in the North Atlantic, north of the main transport pathways). Some of the highest IAV variability occurs over ocean regions, especially in the Southern Hemisphere. There is much more seasonal variability than IAV variability in most locations in the Northern Hemisphere (Fig. 6b), with smaller ratios of seasonal to IAV variability over the southwest US, North Atlantic to Northern Europe, and across large parts of the Southern Hemisphere (Fig. 6b). The deposition and AOD IAV variability have similar patterns to the concentration, with a slightly higher variability in deposition and slightly lower AOD (Fig. 6a vs. Fig. S10a and c), and similar importance of the seasonal cycle (Fig. 6b vs. Fig. S10b and d). As discussed in Sect. 3.3, for the CAM4 and CAM5 model simulations, some of this enhanced Southern Hemisphere variability could be due to the tuning of the source areas, because the dust sources were not consistently active enough (Albani et al., 2014). If we consider only the models in which the Southern Hemisphere dust sources did not have to be increased – GCHEM (MERRA) and MATCH (NCEP) – then the monthly mean variability in the South Atlantic is similar to the North Atlantic (Fig. 6c), but there still tends to be a smaller proportion of the variability from seasonal variability, and thus a more important role for interannual variability, in the South Atlantic, Indian or Pacific oceans than in the Northern Hemisphere oceans (Fig. 6d). Some of the limited observational data supports strong interannual variability in the Southern Hemisphere, although not as strong as some of the model versions (Sect. 3.3).

Next we consider how similar the temporal variability is in the model simulations covering the same time period. If two model simulations are temporally correlated, it implies the timing of the monthly mean variability in the models is similar. Of course, to obtain the fraction of the variability that is similar, the correlation coefficient needs to be squared (if we assume a Gaussian distribution in the model output), which means that even a statistically significant (at 95 %) high correlation of 0.8 (for 16 different years) only implies that 60 % of the variability is similar. However, the correlation is a useful way to consider how similar the simulations are in their variability. The correlations between the model simulations for the surface concentration suggest that the models simulate similar IAV variability over some of the globe, but over most of the globe, there is no statistically significant correlation (Fig. 7). The strongest correlations occur in the model simulations with reanalysis-driven simulations (Fig. 7a, b, d and e), and the simulations with time-varying SSTs (AMIP) were more different (Fig. 7c and f). This suggests that sea surface temperature forcings are not the only important driver for the dust cycle. Notice that simulations with the same model but different winds (CAM4 (MERRA) vs. CAM4 (NCEP); Fig. 7a) had similar correlation coefficients to using different winds and model framework (e.g., CAM4 (MERRA) vs. MATCH (NCEP); Fig. 7e) or different models with the same winds (e.g., CAM4 (MERRA) vs. GCHEM (MERRA); Fig. 7d). This is made more clear when we average the correlations across CAM4 reanalysis models and compare to simulations using different model frameworks driven with the same meteorological data (Fig. 8a vs. Fig. 8b), which show similar patterns of correlations. This suggests that both model framework and winds contribute to variability, and perhaps in a similar, but not additive magnitude.

We can explore the drivers of interannual variability by focusing on the average correlation between the CAM4 simulations driven by reanalysis (CAM4-RE average) and the North Atlantic Oscillation (NAO) and the El Niño–Southern Oscillation (ENSO) climate indices (Fig. 8c an d). These show correlations similar to previous studies (e.g., Moulin et al., 1997; Mahowald et al., 2003), and suggest some correlation between NAO and ENSO. Because we are using a relatively short time period (16 years), these signals do not show as statistically significantly as if we use a longer time period, but the same models (e.g., MATCH in Mahowald et al., 2003, included 22 years) have shown a similar pattern in previous studies. There is much more coherence in the simulated variability from the reanalysis winds, than seen in the NAO or ENSO (Fig. 8a vs. Fig. 8c and d). This is also consistent with the lower correlation between the SST-driven model simulations (AMIP-style) (Fig. 8e). There are much higher correlations between model results when we use reanalysis winds compared to forcing with only sea-surface temperatures, indicating the value of using reanalysis datasets to obtain more robust results. Notice that there is a much stronger correlation between models if we consider the seasonal cycle (Fig. 8f), indicating the difficulty the models have with simulating IAV compared with the seasonal cycle. This is consistent with previous studies showing similar simulation of seasonal cycle across many models (e.g., Huneeus et al., 2011).

Surprisingly in some remote ocean regions, the models are simulating similar interannual variability (notably, parts of the Atlantic, Pacific and Indian Oceans), although this could be spurious due to the short time period considered (Fig. 8). There are some statistically significant trends in the model simulations over the 1990–2005 time period, as seen in Barbados (Sect. 3.2) and the nearby North Atlantic and some parts of northern Africa (Fig. 4), which may be responsible for some of this coherence. The patterns and magnitude of correlation coefficients is similar for deposition and AOD in the models (Fig. S11).

A comparison of other aerosols in two of the CAM4-reanalysis-based simulations available here (Fig. S12) is consistent with the idea that dust is more highly variable. For other aerosol types, especially BC, OC and SO4, which include in this study no IAV in the sources, there is some correlation between the models driven by different meteorology far from the sources as well as close (Fig. S12). We will next discuss regional averages to understand how similarly ocean basin averages are simulated, to see if these IAV correlations in some regions are large enough to provide coherent basin estimates.

As discussed in the cases of the Tropical North Atlantic and South America (Sects. 3.2 and 3.3), as well as in previous studies (Tegen and Miller, 1998), some of the variability in dust comes from the source regions. Looking across the model simulations considered here, we see strong IAV in many of the source regions, with the strongest IAV in the smallest source regions, as seen previously (Tegen and Miller, 1998; Mahowald et al., 2003) (Fig. 9). Only the western Sahel source (Sect. 3.2) is simulated to have a statistically significant trend in all the model simulations (Table 4, also seen in Figs. 4 and 9). There are strong increases in some of the model simulations of the Australian source, consistent with the observed increase in drought over this time period (Cai et al., 2014), although we do not know of dust observations verifying this. For example, visibility data extending through 2003 do not support an increase in dust-source strength in Australia (Mahowald et al., 2007). Previous studies have shown that there are decreases in dust from South America over the 1990–2005 period in some models (Doney et al., 2009), but these are not shown in all the model versions or supported by robust observational data (Doney et al., 2009). Yu et al. (2015) show evidence for strong decadal variability in the Saudi Arabian source over a different time period than considered here, with an increase between 2000 and 2015, arguing that a drought in the Fertile Crescent is responsible for the increase after 2000. The model simulations included here show a lower dust source during 2000–2005 (Fig. 9), consistent with their results, and correlation between precipitation and dust source in these simulations (Table 7). Considering the 1990–2005 period, on a global average, some models simulate an increase in the global dust source, other models simulate a decrease, suggesting no clear trends from the modeling of the global dust cycle over this time period (Fig. 9).

If we consider regional averages, there are moderate correlations in time (0.4–0.8) in the annual mean source strength, except for the Sahel region (0.13), suggesting they simulate similar interannual variability (Table 6; Fig. 9). Although the emphasis of this paper is on the temporal variability, there are significant differences in the climatological mean source strengths in the models used here (Table 6), highlighting the uncertainties in dust sources. The larger sources (such as northern Africa and the Sahel) have mean source strengths varying by 25 % while the smaller sources (such as North and South America) vary up to 160 %, just due to differences in the meteorology, using the same CAM4 model and observational constraints (Albani et al., 2014).

Focusing on the drivers of the CAM4-modeled variation in sources suggests that LAI has the strongest correlation with IAV in sources for several source regions (Australia, South Africa and South America (Argentina), while surface winds have the highest correlations for East Asia, Middle East, northern Africa and the western Sahel (Table 7). It is reassuring that the model winds have high correlations with IAV source strength in the model for East Asia, for there is a strong correlation in the current climate observations between winds and sources in this region (e.g., Sun et al., 2001), as well as speculation that past climate variability in winds from East Asia is sensitive to synoptic-scale wind events (e.g., Roe, 2008;McGee et al., 2010). Soil moisture has the highest correlation for North America. Notice that IAV in LAI is likely to be a strong function of soil moisture, and precipitation (Table 8), and LAI may cause changes in surface roughness and therefore winds (Cowie et al., 2013), so these variables are all likely to be related. There are trends across this relatively short time period of a few of the source regions and variables, averaged across all the models (Table S7), but longer records tend to suggest oscillation in dust-related variables: for example, the downward trend in dust in the Sahel from the 1980s followed a strong upward trend between the 1960s and the 1980s (Prospero and Lamb, 2003), and indeed there may have been even longer trends in dust from northern Africa (Mulitza et al., 2010). Thus, trends in the short time period considered here (1982–2008) may not necessarily be representative of the longer-term trends.

The current generation of Earth system models have a great deal of difficulty in simulating not only precipitation (as discussed in Sect. 3.2) but also LAI (e.g., Sitch et al., 2015; Mahowald et al., 2016), and thus this strong dependence on difficult-to-simulate variables may decrease our ability to simulate interannual variability. Note that using satellite-retrieved vegetation (e.g., Zhu et al., 2013), as done in some models (e.g., Ridley et al., 2014), may remove model-derived uncertainties, but the satellite-retrieved vegetation has large uncertainties, especially in regions with low LAI, and does not do a good job of detecting brown vegetation, which is very important in resisting dust entrainment (e.g., Okin et al., 2001). This suggests that simulation of the surface conditions (e.g., vegetation, soil moisture, surface winds) in the source regions is likely to limit our ability to accurately simulate IAV in dust.

Downwind of the source regions, there is some coherence in the simulated variability in the surface concentrations as well (Table 8), especially in the North Atlantic, North Pacific, Equatorial Atlantic, South Pacific and South Indian Ocean (with correlation coefficients between different CAM4-RE simulations averaging between 0.46 to 075), but in other regions there is less coherence. The sources which dominate the surface concentration, deposition and AOD in different downwind regions were not diagnosed in this study, but were previously shown for the mean in related model simulations (see Albani et al., 2014; Fig. S1), and suggest source–receptor-type relationships consistent with previous studies (e.g., Tanaka and Chiba, 2006; Mahowald, 2007). Those studies suggest that, as expected, northern African sources dominate the North Atlantic dust burden (or conditions), and East Asian and Central Asian sources dominate the North Pacific. The Central Asian sources are important for the North Indian Ocean. The Southern Hemisphere sources tend to dominate the regions just downwind of the sources (Fig. S1, Albani et al., 2014). These results are consistent with the available source provenance data, which were used to `tune' the CAM4 simulations (see Albani et al., 2014 for more details).

For the downwind regions, we can consider the importance of the climate indices in the time series (Fig. 10; Table 8). If we examine the regional correlation coefficients of dust surface concentration to the NAO, there is very little correlation across this 16-year period for the North Atlantic (Table 8 and Fig. 8c). Previously studies showed a larger contribution, which might be due to the short time series used here (Moulin et al., 1997) (Mahowald et al., 2003; Ginoux et al., 2004). The largest magnitude correlations are seen in regions remote from the NAO (the Antarctic, for example, with an anti-correlation of -0.42), which may be due to spurious correlations (Table 8). If we consider ENSO (Table 8), we see that the strongest correlations occur in the ocean basins where this oscillation dominates the physics (also seen in Fig. 8d). The North Pacific had the highest correlation coefficient (0.62), followed by the North Atlantic (0.45) and Equatorial Pacific (0.42). These results, for the shorter term oscillation of ENSO in contrast to the decadal oscillations from NAO, are more similar to previous results (e.g., Mahowald et al., 2003).

For some applications (e.g., IAV in iron fluxes on biogeochemistry or IAV in dust contributions to AOD), deposition and AOD are more important (Streets et al., 2009; Doney et al., 2009), and thus we briefly consider the time series of these model fields (Figs. S13 and S14). The mean deposition from the different model simulations can vary widely (Table S9), as seen in the source strengths (Table 6) and previous studies (e.g., Huneeus et al., 2011). Downwind of the large source regions (e.g., North Atlantic, Central North Atlantic, Equatorial Atlantic and Northern and Equatorial Indian Ocean) the standard deviations between CAM4-RE climatology mean are the lowest (7–25 %), and they are largest in the remote ocean regions, like the Southern Ocean (100 %) (Table S9). The standard deviation between models is slightly larger if all models are included (Table S9). Similarly, for the AOD in the ocean basins, the difference in model simulations is smallest close to the source regions (20 %) and largest in the remote ocean regions (100 %) (Table S10).

Here we emphasize the temporal variability, and the comparison of the CAM4-RE model simulations suggest in many basins there are consistent signals, with correlations in net deposition above 0.3 in most basins, with the exception of North Indian and South Atlantic (Table S9; Figs. S13 and S14). Interestingly, AOD is consistent (r > 0.3) in different basins, with the North Central Pacific and North Atlantic Equatorial Pacific having the lowest correlations. This highlights the disconnect between AOD and deposition, which can make diagnosing deposition variability from AOD difficult, as noted previously (e.g., Mahowald et al., 2003). Note even in the basin with the most consistent simulations (0.68 in the North Atlantic), the variability in deposition, simulated similarly in the models, represents only 50 % of the variability (if we assume for simplicity Gaussian distributions, which is not true of these values, suggesting even less of the variability is similarly simulated).

The large variability in dust implies that it may be difficult to constrain the dust cycle from limited observations. While we have satellite data, we can only use that data to constrain dust when it is the dominant aerosol, which occurs only in limited regions just downwind of major sources like northern Africa (Mahowald et al., 2007). Over much of the ocean, we only have individual daily-averaged values from cruise data (Baker et al., 2006; Buck et al., 2006; Sholkovitz et al., 2012). Previous model studies have shown that over much of the ocean, modeled daily-averaged dust concentrations will tend to underestimate the annual average, and only be within a factor of 10 to 2 of the true modeled average (Mahowald et al., 2008). Here we consider how many monthly means are required to obtain an estimate of the annual mean that is within 1 standard deviation of the true model annual mean value (Fig. 11). Over most of the globe, the number of monthly mean observations is 8–12, or almost a full seasonal cycle, as expected. But in regions with large variability (Fig. 6), longer time periods of more than 2 full years are required to obtain a mean and standard deviation including the true mean (Fig. 11). Note that here we assume that there is no trend or significant change in the dust cycle. Characterizations of changes in dust show that there are interesting trends over the longer term, which requires longer records (Prospero and Lamb, 2003; Ridley et al., 2014).