Fig. 6. PS of observed Sahelian precipitation (black) and associated 95% confidence interval (black shading) compared to the PS of amip-piF simulations (a) and amip-hist simulations (b). As in Figure 4, mean PS by model are colored by average yearly precipitation, where brown is drier than observed, grey is observed, and turquoise is wetter than observed. The mean PS across models is displayed in orange for amip-piF (a) and in green for amip-hist (b). The dashed lines show the PS of the MMMs with associated 95% confidence intervals (colored shaded areas).
The curves colored brown to turquoise in Figure 6 show the average by model of the PS of individual simulations, colored by climatological Sahelian precipitation bias. We note that wet-biased simulations (turquoise) have more power than dry-biased simulations (brown), consistent with the expected relation between the mean and variance of precipitation. The tiered mean over these PS is presented in solid orange; it contains atmospheric IV (\(\overrightarrow{a}\)) in addition to SST-forced variability (\(\overrightarrow{t}\)). Though it is not statistically different from the MMM PS, atmospheric white noise gives it slightly more power at all frequencies, and thus it is clearly consistent with the observed PS (black). Global SST forcing, while unable to explain much of observed high frequency variability in Sahelian precipitation (note the low power of the dashed orange curve at periods below 20 years), is able to reproduce the pattern and, in combination with atmospheric IV, the full magnitude of observed multi-decadal precipitation variability.
We now estimate the “fast” precipitation response to ALL in the CMIP6 AMIP simulations (Figure 5c, purple, \(\overrightarrow{f}\)) by subtracting the MMM of amip-piF simulations (a, orange) from that of amip-hist simulations (b, green), the latter of which are forced with historical SST and historical external radiative forcing. The AMIP “fast” MMM shows some episodic variability that is consistent with the coupled NAT MMM, and a wetting trend after 1985. On its own, it is only weakly correlated to observations (r = 0.12, sRMSE = 1.02), and it has relatively low amplitude. When combined with SST forcing in the amip-hist simulations, it has little effect: correlation stays at 0.60 and sRMSE is reduced from 0.81 only to 0.80 (compare green and orange curves in Figure 3) and spectral properties are virtually unchanged (Figure 6). The best linear fit to observed precipitation would combine the amip-piF MMM with the fast response to forcing scaled down by a factor of \(0.3\pm 0.2\). The fast response may be overestimated in AMIP simulations because the radiative forcing has directly contributed to generating observed SST which is prescribed in the simulations, and because the magnitude of the radiative forcing itself may be overestimated, as suggested by Menary et al. (2020).
The high performance of the amip-piF simulations and the small impact of the potentially overestimated fast response to forcing suggest that the principal deficiency in simulating low-frequency Sahelian precipitation variability in coupled models stems from a deficiency in simulating the observed combination of forced and internal variability in SST, and not from a failure to reproduce the observed teleconnection strength or fast response to forcing.
c. The NARI Teleconnection: AMIP Simulations and Observations (\(\overrightarrow{t}\))
We next determine the strength of the linear NARI-Sahel teleconnection and investigate how well it represents the effect of global SST on Sahel precipitation in simulations and observations. Observed NARI anomalies relative to the 1901-1950 mean are presented in Figure 5a in light blue on the right ordinates. NARI correlates well with SST-forced Sahelian precipitation in the amip-piF simulations (orange, left ordinates;\(r\ =\ 0.52\pm 0.10,\ r=0.60\ for\ the\ actual\ MMM\)), but still leaves 64% of its variance unexplained, suggesting influences from other SST patterns or non-linear or non-stationary effects (Losada et al. 2012). Some of the unexplained variance is at faster timescales than those of our interest, but not all. Let’s assume that the influences of NARI and other ocean basins on Sahel precipitation are linear and add linearly, and that the NARI teleconnection is unconfounded by the influence of other ocean basins; then we can measure the strength of the NARI teleconnection by the regression coefficient of the amip-piF precipitation MMM, which contains only SST-forced variability, on NARI. This calculation yields a regression slope of \(0.87\pm 0.26\frac{\text{mm}}{day*C}\). This value is affected by both high- and low-frequency variability, which is appropriate if the teleconnection is, indeed, linear. The left ordinates in Figure 5a are scaled relative to the right ordinates by this teleconnection strength so that, when read on the left ordinates, the light blue curve represents the expected precipitation response to NARI. This view highlights how NARI captures the timing of simulated low-frequency variability, even though it fails to explain the full magnitude of simulated dry anomalies after 1975. In the rest of this paper we use the NARI teleconnection as the best linear representative of the simulated influence of SST on Sahel precipitation in the 20th century.
The teleconnection strength calculated from the amip-piF simulations is not directly comparable to observations, because the latter includes the fast precipitation response to forcing, which can confound estimates of the teleconnection. A comparison can be drawn between the apparent teleconnection strength in the amip-hist simulations (\(0.93\pm 0.41\)) and in observations (1.04). The consistency lends credence to our previous suggestion that simulated SST teleconnections to Sahel rainfall appear to have the appropriate strength in CMIP6, at least in the amip simulations.
d. Forced and Internal SST Variability in Coupled Simulations (\(\overrightarrow{s}\) and \(\overrightarrow{o}\))
We now examine simulation of forced (\(\overrightarrow{s}\)) and internal (\(\overrightarrow{o}\)) SST variability. Figure 7 compares observations (black) to the simulated SST response to forcing (\(\overrightarrow{s}\))—represented by MMM anomalies (colors)—for NARI (right column) and its constituent ocean basins – the North Atlantic (NA, left column) and the Global Tropics (GT, middle column). The yellow shaded areas show the bootstrapping 95% confidence intervals of the piC simulations for statistical significance, while the other shaded areas denote uncertainty in the CMIP5 and CMIP6 MMMs. As above, CMIP5 MMM anomalies are presented in dotted curves and CMIP6 in solid curves, color-coded according to their forcing.