Fig. 1. Causal diagram relating external forcings (F), internal variability (IV), sea surface temperatures (SST), and Sahelian precipitation (P) via directional causal arrows. Unobserved variables and their causal effects are presented with dashed lines, while observed variables are presented with solid lines.
Characterization of these path components has been controversial. Firstly, separating the SST response to forcing (\(\overrightarrow{s}\)) from SST variability internal to the climate system (\(\overrightarrow{o}\)) has proven difficult (top of diagram). In particular, there is significant debate over whether observed AMV is a response to external forcing (Booth et al. 2012; Chang et al. 2011; Hua et al. 2019; Menary et al. 2020; Rotstayn and Lohmann 2002) or mainly an expression of IV in the Atlantic Meridional Overturning Circulation (AMOC, Han et al. 2016; Knight et al. 2005; Qin et al. 2020; Rahmstorf et al. 2015; Sutton and Hodson 2005; Ting et al. 2009; Yan et al. 2019; Zhang 2017; Zhang et al. 2016; Zhang et al. 2013) that is underestimated in models (Yan et al. 2018). This debate has been hard to resolve partially because IV in AMOC and aerosol forcing may have coincided by chance in the 20thcentury (Qin et al. 2020). Next, examine the bottom of the diagram. The effect of the observed SST field on Sahel precipitation \((\overrightarrow{t})\) can be directly estimated using atmosphere-only simulations, but while these simulations capture the pattern of observed Sahel precipitation variability, many fail to capture its full magnitude (Biasutti 2019; e.g. Hoerling et al. 2006; Scaife et al. 2009). This could reflect an underestimate in climate models of the strength of SST teleconnections, which could be resolution dependent (Vellinga et al. 2016), or of land-climate feedbacks that amplify the teleconnections (\(\overrightarrow{t}\)), such as vegetation changes (Kucharski et al. 2013). But it could also reflect a significant additional role in the observations for a fast response to forcing (\(\overrightarrow{f}\)) that confounds the SST-forced signal\([P\leftarrow F\rightarrow SST\rightarrow P\); see Pearl et al. (2016) for notation] or coincides with it by chance.
To examine the path components in coupled simulations, we need a parsimonious characterization of the relationship between SST and Sahel precipitation. Giannini et al. (2013) and Giannini and Kaplan (2019, hereafter GK19) identify the North Atlantic Relative Index (NARI), defined as the difference between average SST in the North Atlantic (NA) and in the Global Tropics (GT), as the dominant SST indicator of 20th century Sahel rainfall in observations and CMIP5 simulations. There are two main theories relating NARI to Sahelian precipitation (see Biasutti 2019; Hill 2019 for reviews of competing theories of monsoon rainfall changes). In the first, the “local view” (Giannini 2010), warming of GT causes even stronger warming throughout the tropical upper troposphere (Knutson and Manabe 1995; Parhi et al. 2016; Sobel et al. 2002), increasing thermodynamic stability across the tropics and inhibiting convection in an “upped ante” (Giannini and Kaplan 2019; Neelin et al. 2003) or “tropospheric stabilization” (Giannini et al. 2008; Lu 2009) mechanism. Warming of NA, on the other hand, is expected to thermodynamically increase moisture supply to the Sahel by increasing specific humidity over the NA, and thus destabilize the atmospheric column from the bottom up (GK19). The second theory interprets the relationship of Sahel precipitation to NARI, or, similarly, to the Atlantic meridional temperature gradient or the Interhemispheric Temperature Difference (ITD), as the result of an energetically-driven shift in the Intertropical Convergence Zone (ITCZ, Donohoe et al. 2013; Kang et al. 2009; Kang et al. 2008; Knight et al. 2006; Schneider et al. 2014) and the African rainbelt (e.g. Adam et al. 2016; Biasutti et al. 2018; Camberlin et al. 2001; Caminade and Terray 2010; Hoerling et al. 2006; Hua et al. 2019; Pomposi et al. 2015; Westervelt et al. 2017). According to both theories, an increase in NARI should wet the Sahel while a decrease causes drying. Given the prominence of the NARI teleconnection in the 20th century and the assumption of linearity, we approximate the full slow response as the product of the NARI response to external forcing and the strength of the NARI-Sahel teleconnection.
This paper is organized as follows: Section 2 provides details on the simulations and observational data used in this analysis while Section 3 discusses the methods. In Section 4.a, we update H20’s analysis to the Coupled Model Intercomparison Project phase 6 (CMIP6, Eyring et al. 2016), examining the total response to forcing (all paths from F to P) and internal variability (all paths from IV to P). We then evaluate the performance of the CMIP6 AMIP simulations, decomposing them into the path components from the bottom half of Figure 1 \((\overrightarrow{t}\),\(\overrightarrow{f}\), and \(\overrightarrow{a}\)) in Section 4.b, and focusing on the NARI teleconnection in Section 4.c. Section 4.d decomposes coupled simulations of NARI into the path components from the top half of Figure 1 (\(\overrightarrow{s}\) and\(\overrightarrow{o}\)), while Section 4.e evaluates the consistency of the NARI teleconnection established in Section 4.c with coupled simulations. Finally, in Section 4.f, we use simulated NARI and the simulated NARI teleconnection to decompose the total response of Sahel precipitation to external forcing in coupled simulations (examined in Section 4.a) into fast and slow components. We discuss how our results fit in with the existing literature in Section 5 before concluding in Section 6.
2. Data
We examine coupled “historical” simulations from CMIP5 (Taylor et al. 2012) and CMIP6 (Eyring et al. 2016) forced with four sets of forcing agents—AA alone, natural forcing alone (NAT, which includes VA as well as solar and orbital forcings), GHG alone, and all three simultaneously (ALL)—as well as pre-Industrial control (piC) simulations, in which all external forcing agents are held constant at pre-Industrial levels. We additionally examine CMIP6 amip-piForcing (amip-piF) simulations, in which atmospheric models are forced solely with observed SST, and CMIP6 amip-hist simulations, which are forced with observed SST and historical ALL radiative forcing. Calculations with CMIP5 utilize the period between 1901 and 2003 while calculations with CMIP6 extend to 2014.
In H20, we used all available institutions for each forcing subset. Here, in order to provide a more stringent comparison of the effects of different forcing agents, we exclude institutions from the coupled ensemble that do not provide AA, GHG, and ALL simulations, and from the AMIP ensemble if they do not provide both amip-piForcing and amip-hist simulations. We additionally exclude piC simulations that are shorter than the historical simulations as well as any simulations with data quality issues. Tables S1-S3 enumerate the simulations used in this analysis.
Precipitation observations are from the Global Precipitation Climatology Center (GPCC, Becker et al. 2013) version2018, and SST observations are from the National Oceanic and Atmospheric Administration’s (NOAA) Extended Reconstructed Sea Surface Temperature, Version 5 (ERSSTv5, Huang et al. 2017).
We analyze precipitation over the Sahel (12°-18°N and 20°W-40°E) and the SST indices of GK19: the North Atlantic (NA, 10°-40°N and 75°-15°W), the Global Tropics (GT, ocean surface in the latitude band 20°S-20°N), and the North Atlantic Relative index (NARI, the difference between NA and GT). All indices are spatially- and seasonally-averaged for July-September (JAS).
3. Methods
The multi-model mean (MMM) for a set of simulations consists of a 3-tiered weighted average over (1) individual simulations (runs) from each model, (2) models from each research institution, and (3) institutions in that ensemble. Details of the weighting are provided in H20; the results are robust to differences in weighting. Time series are not detrended, and anomalies are calculated relative to the period 1901-1950.
To evaluate the performance of the simulations relative to observations, we compute correlations (r), which capture similarity in frequency and phase, and root mean squared errors standardized by observed variance (sRMSE), which measure yearly differences in magnitude between the simulations and observations. An sRMSE of 0 represents a perfect match between simulations and observations, and 1 would result from comparing the observations with a constant time series.
To estimate uncertainty in the forced MMMs and associated metrics, we apply a bootstrapping technique to the last tier of the MMM as described in H20, yielding a probability distribution function (pdf) about the MMM and each metric. Due to the finite number of simulations, these pdfs underestimate the true magnitude of the uncertainty. We evaluate significance by applying a randomized bootstrapping technique, which increases the effective sample size, to the piC simulations with one significant improvement over H20: instead of using just one subset of each piC simulation at a random offset in the first tier of the MMM in each bootstrapping iteration, we take enough subsets to match the number of that model’s historical runs. Done this way, the confidence intervals calculated using piC simulations accurately represent noise in the forced MMMs. PiC pdfs from the same ensemble differ slightly because many institutions provide a different number of simulations for different subsets of forcing agents (see Table S2). Where the piC pdfs and confidence intervals are similar enough, they are presented together with a single grey dotted curve and dashed line; when they differ, they are presented in the colors associated with the relevant forcings.
We perform a residual consistency test, which compares the power spectra (PS) of individual simulations to that of observations, with one significant modification over H20: we calculate the PS using the multi-taper method. Confidence intervals for the PS for observations and MMMs are given by the multi-taper method, without accounting for the uncertainty in the MMMs themselves. Mean PS by model are colored by climatological rainfall bias given by those simulations. The multi-model mean of these PS, or the “tiered mean”, is calculated using the three tiers from the definition of the MMM, but without weights, since spectral power is not attenuated when averaging PS.
4. Results
a. Changes in CMIP6: Total Precipitation Response to Forcing and Internal Variability
If Sahelian precipitation is a linear combination of IV in the coupled climate system and variability forced by external agents, then the MMM over coupled simulations with differing initial conditions filters out atmospheric and oceanic IV (\(\overrightarrow{a}\) and\(\overrightarrow{o}\)), leaving the fast and slow precipitation responses to external radiative forcing (\(\overrightarrow{f}\) and\(F\rightarrow SST\rightarrow P\)). Figure 2 compares observed Sahelian precipitation anomalies (black, left ordinates) to the MMM anomalies of simulated Sahelian precipitation (right, amplified colored ordinates) in CMIP5 (dotted curves) and CMIP6 (solid curves) for four sets of forcing agents: ALL (a, blue), AA (b, magenta), natural forcing (c, “NAT,” brown and red), and GHG (d, green). The figure also presents the bootstrapping 95% confidence intervals of the forced CMIP6 MMMs (blue, magenta, brown, and green shaded areas) and of MMMs over the CMIP6 piC simulations (yellow shaded areas) on the right ordinates. The width of the yellow shaded areas represents the magnitude of noise deriving from coincident IV in the MMMs. Differences in its width between panels arise from varying numbers of simulations for the different forcing subsets (see Methods and Table S2).