We build on this by employing the statistical techniques of multivariate detection and attribution to precipitation at a regional scale. Exploiting the coherent response to forcing across multiple variables, regions, or scales may both enhance the signal of anthropogenic forcing and decrease the noise, by rendering internal variability less likely to project by chance on the response to forcing. Here, we will use the characteristics of Sahel rainfall to create a multidimensional fingerprint that captures coherent aspects of expected forced change.

To what extent, then, do recent Sahel rainfall trends reflect the recovery from aerosol-induced drought versus the response to increasing greenhouse gas forcing? And is either of these responses distinguishable from internal variability? Previous work has attempted to separate the roles of these forcings by linking them to different SST warming patterns [ 12 , 31 ]. Bonfils et al (in revision) employed a global-scale analysis of temperature, precipitation, and aridity to distinguish two modes of externally-forced fingerprints associated with greenhouse gas and aerosol forcing.

While it is difficult to formally attribute these observed changes to external forcing, they do appear to capture several aspects of the expected regional precipitation response to greenhouse gas forcing. An increase in mean and extreme rainfall intensity is a robust consequence of a warmer world, where increased latent heat flux from the surface is balanced by an increase in average precipitation [ 23 ] and the saturation water vapor pressure increases with temperature [ 24 , 25 ]. Moreover, an east-west gradient in forced change is apparent in many climate models, possibly related to the zonal asymmetry in the Sahara Heat Low, an area of low pressure concentrated over the western Sahara. The low-level geostrophic flow into this local minimum advects dry subtropical air to the west and moist tropical air to the eastern Sahel [ 26 ]. Warming strengthens this effect and contributes to drying in the west and wetting in the east: an asymmetry that should be exacerbated as greenhouse gases increase [ 27 ]. Finally, greenhouse gas forcing is expected to affect the seasonality of precipitation [ 28 ], with increases in rainfall largely confined to the late portion of the rainy season [ 29 ], when the barriers to convection in a more stable atmosphere are more easily overcome [ 30 ].

Recent trends in mean Sahel precipitation suggest a recovery from the exceptionally dry conditions of the 1980s. But, while overall Sahel rainfall has increased, the spatiotemporal characteristics of the rainy season are also changing [ 9 ]. By 2007, precipitation in eastern regions of the Sahel had largely recovered, while the west was still considered in drought [ 20 , 21 ]. Moreover, an increase in mean precipitation has also been accompanied by an intensification of individual rainfall events [ 22 ].

In the wake of clean-air legislation passed in North America and western Europe, anthropogenic sulphate aerosol emissions fell and anthropogenic aerosol forcing decreased [ 14 , 15 ]. In the 1990 s, Sahel precipitation began to recover [ 16 , 17 ]. However, the decrease in aerosol emissions has not been accompanied by a concurrent decrease in greenhouse gas emissions, which have continued to rise. To interpret the most recent trends, and to provide reliable projections of future rainfall, it is therefore crucial to disentangle the role of internal variability and multiple external forcings. If, for example, recent positive trends in Sahel rainfall result from a decrease in North America and western European aerosol [ 18 ], then we should not expect them to continue throughout the 21st century. If, however, they are attributable to greenhouse gas emissions [ 19 ], then we might expect future GHG emissions to accelerate existing trends, and plan accordingly.

However, even against this noisy backdrop of internal variability the Sahel has experienced significant multidecadal precipitation changes over the 20th and 21st centuries attributable to external forcing [ 10 , 11 ]. Idealized experiments with a single model attributed the pronounced 1950–1980 drying to external forcing [ 12 ], specifically anthropogenic aerosols. A study using CMIP3 and CMIP5 models and observations found that aerosol-induced cooling over the North Atlantic forces the ITCZ south, displacing the Sahel rain band [ 1 ], although this shift is severely underestimated by climate models. The severest recent drought in the region has been partially attributed to a combination of anthropogenic aerosol and volcanic forcing, notably the 1982 eruption of El Chichón [ 13 ].

Precipitation in the Sahel, the semi-arid region just south of the Sahara desert, affects a large and rapidly growing population. The region, which extends from Senegal in the west to Sudan and Ethiopia in the east, experiences rainfall concentrated in a wet season that runs June-October, with the bulk of precipitation falling in August and September. Spatially, the average rainfall varies sharply with latitude, with much smaller zonal gradients. It is strongly affected by internal climate variability at multiple spatial and temporal scales. Sahel rainfall is affected by the location of the Intertropical Convergence Zone (ITCZ), with increases in rainfall when the ITCZ is shifted anomalously north and drought when it moves south [ 1 ]. The region is also affected by variability in the global oceans [ 2 , 3 ]: for example, the warming of the tropical troposphere during an El Niño event can suppress regional convection by enhancing atmospheric stability, while warming in the Atlantic or the Mediterranean can bring moisture to the region and strengthen the monsoon [ 4 – 6 ]. Despite these linkages to large-scale phenomena, however, aggregate rainfall in the Sahel results from short-lived weather systems on smaller time scales [ 7 ]. Understanding and simulating variability in Sahel rainfall therefore requires an integrated perspective of the drivers of this variability on multiple spatiotemporal scales [ 8 , 9 ].

The simplest possible approach to detecting climate changes is to calculate the trends in regional or global mean variables and compare them to similar-length trends in unforced variability estimated by climate models [32, 33]. If such trends are deemed unusual in the context of model-estimated internal variability by some statistical test, they may be considered detectable. However, detecting the signatures of external forcings on regional climate is challenging for several reasons: internal variability may be considerable on regional scales, observational uncertainty may be large, and in some regions, high-quality observations do not exist over long timescales. Several authors [34, 35] have therefore advocated a process-based perspective that captures the specific spatial or seasonal aspects of the forced response in order to enhance the signal and decrease the noise. In detection and attribution research, the main goal is to separate the forced responses ('fingerprints') from the noise. In the literature, different statistical/numerical techniques exist to estimate these fingerprints (e.g. least-squares regression, optimal fingerprints with or without the need for empirical orthogonal function (EOF) truncation and others methods [36–38]) . These may be trends, as discussed above, characteristic time series [39], or spatial patterns that capture the forced response [40]. Here, we will treat the 'fingerprint' as a spatial pattern and define the fingerprint of a particular external forcing or collection of forcings as the leading EOF of the average of model simulations run subject to those forcings [41]. Because the averaging process damps internal variability, the leading EOF generally explains a large proportion of the total variance [42, 43].

To track expected and observed spatiotemporal changes, we consider four indicators: two variables (monthly mean precipitation, hereafter PRMEAN) and the fraction of rainy days, defined as days where rainfall exceeds 1 mm and hereafter referred to as R1) averaged over two regions (the central-eastern portion of the Sahel (east of the prime meridian) and the western Sahel (west of the prime meridian)). These quantities are calculated for CMIP5 historical simulations beginning in 1901. Because these historical simulations end in 2005, we extend them to the year 2100 by splicing with the corresponding RCP8.5 simulation beginning in 2006; we will refer to these extended simulations as H85. A list of all model simulations that provided relevant data for the historical and RCP8.5 simulations is provided in table B1. Where multiple ensemble members are present, we calculate the multi-model average by first averaging over ensembles and then over models.

To ensure all variables carry the same units, we create z-scores by normalizing each variable X(t) by a measure of noise . This is obtained by calculating monthly anomalies in X in the first 200 years of every pre-industrial control simulation, concatenating the resulting time series, and taking the standard deviation of the concatenated values.

To calculate the fingerprint, we construct the state vector

and perform the singular value decomposition

where is a diagonal matrix whose elements represent the eigenvalues. The unitary matrix represents the multivariate EOFs, while contains the principal components. The fingerprint is then defined as the leading multivariate EOF [44, 45] and has 48 dimensions: it reflects changes in four variables over the twelve months of the calendar year. This fingerprint captures the model-predicted response to external forcing over multiple aspects of the Sahel rainy season.

The leading EOF of the H85 simulations is non-stationary: the fingerprint of external forcing varies with time because the forcings themselves vary with time. Figure 1 shows the fingerprints calculated from the H85 simulations over the 20th (a) and 21st (b) centuries. The 20th century fingerprint (hereafter 20CEN) is characterized by a symmetric decrease in precipitation in the rainy season across the eastern and western Sahel, and by a commensurate decline in the monthly fraction of rainy days. The 21st century fingerprint (21CEN), by contrast, is characterized by strong seasonality and spatial differences (figure 1(b)), as has been noted previously [46]. In the eastern Sahel, rainfall increases throughout the rainy season. In the west, however, the pattern of change is characterized by a decrease in precipitation early in the rainy season and a smaller increase towards its end. The fingerprint is also characterized by changes in rainfall frequency, as measured by the total number of rainy days. The western Sahel experiences a decrease in the proportion of rainy days throughout the spring, summer, and fall, while the eastern Sahel experiences decreases in the proportion of rainy days that are larger (and, in July, of opposite sign) than the changes in precipitation. The 21CEN fingerprint is nearly identical to the leading EOF calculated from the full 1901-2100 time period (supplementary figure A1 (stacks.iop.org/ERL/15/084023/mmedia)), while the 20CEN fingerprint strongly resembles the second EOF.

Figure 1. (a) Multi-variate fingerprint of forced changes in Sahel rainfall in the H85 simulations calculated over 1900-1999 (20CEN); solid lines depict total precipitation; dotted lines depict frequency of rainy days; purple is for central and eastern Sahel (east of the prime meridian) and orange is for the western Sahel. (b) Same as in (a), but over the period 2000-2099 (21CEN). (c) The principal component associated with the 20CEN fingerprint. (d) As in (c), but for 21CEN. Download figure: Standard image High-resolution image Export PowerPoint slide

Here, we will argue that the 20CEN fingerprint largely captures the multi-model mean regional response to aerosols, while 21CEN captures the regional response to greenhouse gases. Aerosol forcing is believed to primarily affect Sahel precipitation remotely [1], by cooling the North Atlantic and forcing the ITCZ southward. This leads to a decrease in precipitation in the rainy season throughout the entire region: the response captured in the 20CEN fingerprint. The associated principal component (figure 1(c)) tracks the temporal evolution of aerosol forcing, increasing through much of the 20th century before peaking around 1980 and then decreasing. Greenhouse gas forcing dominates the RCP8.5 scenario, and the principal component associated with the 21CEN fingerprint (figure 1(d)) reflects the monotonic increase in greenhouse gas emissions over the 21st century. The fingerprint itself captures many of the theoretically-expected characteristics of the response to greenhouse gas forcing: the asymmetry between the eastern and western Sahel, the seasonal variations, and the decoupling of mean precipitation change and number of rainy days. While the choice of the year 2000 as the dividing point between these two fingerprints is somewhat arbitrary, it does capture the fact that western European and North Atlantic aerosols peaked and declined over the first period, and that the subsequent period is largely dominated by increasing greenhouse gas emission projected in RCP8.5. Other reasonable choices for the boundary between the aerosol-dominated period (for example, 2005, when historical simulations end, or 1990, slightly after the predicted peak in aerosol emissions) yield similar results.

The historical and RCP8.5 simulations are not forced by a single forcing agent, but by changes in anthropogenic (aerosols and greenhouse gases, but also ozone depletion and land-use changes) and natural (orbital changes, solar variability, and volcanic eruptions) forcings. It is therefore desirable to isolate the response to a single forcing by performing targeted simulations. Indeed, the CMIP5 archive contains some single-forcing simulations, namely those in which CO2 is increased at 1% per year (1pctCO2) and the subset of historicalMisc simulations run with only aerosol forcing. But there is a paucity of data in these simulations compared to the historical and RCP8.5 archives. Fewer models provided daily data (required to calculate R1) for 1pctCO2, and only four modeling groups provided the necessary data for the aerosol-only runs. The aerosol-only and CO2-only fingerprints can be calculated from these ensembles of reduced size and are shown in supplementary figure A2. (We note that greenhouse gas-only 'historical GHG' simulations are also available in CMIP5, but we here use 1pctCO2 runs because more simulations of this type are available, and because the signal of greenhouse gas forcing is stronger in 1pctCO2 runs, resulting in a clearer fingerprint less contaminated by internal variability). They are qualitatively similar to the 20CEN and 21CEN fingerprints, respectively, but not exactly alike: the precipitation decreases in the aerosol-only fingerprint are confined to September and October, while the 1pctCO2 fingerprint shows more drying early in the rainy season in the eastern Sahel and does not show an increase late in the rainy season in the west. The differences between single-forcing and the H85 fingerprints, however, are artifacts of the reduced ensemble of models used. When 20CEN is re-calculated using only the models that provided aerosol-only simulations, the spatial correlation between this reduced-ensemble fingerprint and the aerosol-only fingerprint exceeds 0.95. When 21CEN is re-calculated using only the models that provided 1pctCO2 simulations, the spatial correlation between it and the 1pctCO2 fingerprint is 0.82. In order to utilize as many models as possible, here we will rely on the 20CEN fingerprint to approximate the CMIP5 multi-model mean response to aerosols, and on 21CEN to approximate the response to greenhouse gases.

The sensitivity of both fingerprints to the ensemble of models used indicates considerable uncertainty in the model responses to external forcings; this is reinforced by the comparatively small percentage of variance explained by CEN20 (27% of the variance in the 1900-1999 H85 multi-model mean) and CEN21 (50% of variance in the 2000-2099 H85 multi-model mean). Because the averaging process damps internal variability, the leading EOF of the multi-model average generally explains a large proportion of the variance- so why do CEN20 and CEN21 explain so little? First, the historical simulations are also forced by GHG and natural forcings, including volcanic eruptions that are intermittently quite large. These forcings have a response on Sahel rainfall that is non-negligible and not necessarily captured by the leading EOF. Similarly, while dominated, especially at the end of the 21st century, by greenhouse gases, the RCP simulations also include a reduction of anthropogenic aerosol forcing. Second, there is also considerable model disagreement in the response to single forcings: the aerosol-only and 1pctCO2 fingerprints explain only 22% and 36% of the multi-model average variance in the multi-model average of these ensembles, respectively. While this may be due to the smaller sample size of simulation and a less-clear separation between signal and noise, it is well-established that model uncertainties in forced responses may arise from biases in model climatology, particularly in the location of the major features of the circulation [44, 47], from differences in model dynamics [48, 49], uncertainty in the aerosol forcing itself [15], or differences in the model representation of aerosol direct and indirect effects [14].

The multivariate 20CEN and 21CEN fingerprints have the advantage of being nearly orthogonal to one another- the spatial correlation between the two is 0.1. (This can also be seen in the two leading EOFs of the total 1900-2099 H85 simulation, which resemble 21CEN and 20CEN, respectively, and are orthogonal by construction, supplementary figure A1). This property means that, at least in models, it is possible to distinguish between the response to aerosol forcing (particularly as precipitation amounts recover from aerosol-induced declines) and the response to GHG forcing, as the leading response to one forcing will not strongly project on the fingerprint of the other.

The regional precipitation response to external forcing occurs against a backdrop of natural internal variability: climate "noise". Because we have no recent observations of unforced climate, and because paleoclimate proxies represent a climate forced by pre-industrial anthropogenic and natural forcings, we must rely on climate model pre-industrial control simulations (piControl) to characterize this variability [40]. We therefore calculate R1 and PRMEAN for the east and west Sahel in CMIP5 preindustrial control simulations, compute the anomalies, and concatenate the resulting time series. To prevent our results being dominated by models that performed extremely long piControl simulations, here we use only the first 200 years of each simulation. Figure 2 shows the three model-predicted leading noise modes. The primary mode of internal variability, figure 2(a), is likely associated with northward and southward shifts in the ITCZ and is characterized by decreases in precipitation and number of rainy days throughout the entire Sahel in the rainy season. The decrease in rainy days accompanies the decrease in precipitation, indicating no substantial change in the intensity of rainfall. This mode strongly resembles the aerosol-dominated 20CEN fingerprint (the two patterns have a correlation above R = 0.87). The second mode distinguishes between the early and late season but is distinct from the GHG-dominated 21CEN fingerprint in that east and west regions vary together and R1 tracks PMEAN. These results have important implications for the detectability of forced signals: because the 20CEN fingerprint is degenerate with the leading noise mode, models indicate that it will be more difficult to distinguish between the response to aerosols and internal variability. The same difficulty ought not affect the GHG signal.

Figure 2. Leading multi-variate EOFs of Sahel rainfall natural variability as estimated by the CMIP5 pre-industrial control simulations. (a) First noise mode, explaining 17% of the total variance, and (b) the associated PC. (c) Second noise mode, explaining 12% of the total variance, and (d) the associated PC. (e) Third noise mode, explaining 11% of the total variance, and (f) the associated PC. Line styles as in figure 1 and in legend. Download figure: Standard image High-resolution image Export PowerPoint slide

To review, thus far we have presented fingerprints of the Sahel rainfall response to aerosols and greenhouse gases. The two are distinct from one another, indicating that a multivariate approach may be able to distinguish between the response to different forcings [50]. Additionally, the GHG-dominated fingerprint is distinct from the leading modes of internal variability: in models, at least, internal variability does not project strongly on the predicted response to GHG forcing. The same is not true for the aerosol-dominated 20CEN fingerprint: because the response to aerosols strongly resembles the leading mode of internal variability, the models indicate that an aerosol signal must be extremely strong or persistent in order to become detectable over the background of climate noise.