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.