In explaining dynamic causes of changes in amplitude of the zonally anomalous hydrological cycle, we will focus in particular on the stationary-eddy vertical motion at 850 hPa, ω∗850. This is based on the findings of Wills and Schneider (2015, 2016), who show thatP∗−E∗ can be approximated by
P∗−E∗≈ −g−1[qsfc]ω∗850. (4.9)
The intuition behind this is that divergent stationary-eddy circulations carry moisture from the boundary layer to a mean condensation height at about 850 hPa. This has also been shown to govern changes in rms(P∗−E∗) in simple idealized model experiments (Wills and Schneider, 2016),
δrms(P∗−E∗)≈g−1δ([qsfc] rms (ω∗850)). (4.10)
60 S 30 S EQ 30 N 60 N 0
0.005 0.01 0.015 0.02 0.025
latitude rms(ω* 850) (Pa s−1 )
60 S 30 S EQ 30 N 60 N
−0.3
−0.2
−0.1 0 0.1
latitude δ rms(P*−E*) (m yr−1 )
60 S 30 S EQ 30 N 60 N
−15
−10
−5 0 5 10
latitude frac. δ rms(P*−E*) (% K−1 )
a
b
c
60 S 30 S EQ 30 N 60 N
−50 0 50 100
latitude
frac. δ rms(P*−E*) (% K−1 ) implied dynamic
mean dynamic transient simple dynamic
Figure 4.3: a) PAST (solid line) andFUTURE (dashed-line) climatol- ogy of the zonal standard deviation of ω850∗ . Shading shows the range of 95%
(2σ) of the expected sampling vari- ability of this 30-year average based on the year-to-year variance during 1976- 2005. b) Changes in the zonal vari- ance of dynamic and transient-eddy contributions toP∗−E∗, δRMSmdyn
and δRMStrans. These add up to the implied dynamic change, which was shown in Fig. 4.2. Also shown is a simple estimate of the dynamic change (Eq. 4.10). c) Fractional change in variance of the moisture budget terms shown in b).
The climatology of rms(ω∗850), the zonal variance of stationary-eddy vertical motion, is shown in Fig.
4.3. It is highest in the tropics and subtropics. The secondary maxima in the high latitudes come from topographic vertical motions around Greenland and Antarctica.
Figure 4.3b and c show how dynamic changes contribute to the change in rms(P∗−E∗). The stationary-eddy dynamic component (δRMSmdyn, solid red lines) is the leading contribution, espe- cially within 30◦ latitude of the equator. One contribution to this stationary-eddy change is what we will refer to as the simple dynamic change (dashed red lines),
δrms(P∗−E∗)≈g−1[qsfc]δrms (ω∗850). (4.11)
The simple dynamic change shows a slowdown of divergent stationary-eddy circulations. It is a major component of the implied dynamic change (black line) within 15◦ latitude of the equator. This is consistent with ideas that tropical overturning circulations must decrease with global warming such that energetic constraints on global-mean precipitation are satisfied (Betts, 1998; Held and Soden, 2006; Vecchi and Soden, 2007; Schneider et al., 2010). The reductions of stationary-eddy overturning are robust beyond the range of internal variability for some latitude bands in the tropics and southern hemisphere midlatitudes (Fig. 4.3a). Other components of the stationary-eddy dynamic change include correlations of the dynamic change with the climatological dynamic P∗−E∗ contribution and changes in the vertical structure of the atmosphere.
Changes in the zonal variance of transient-eddy moisture flux (δRMStrans, purple lines) are important at higher latitudes. Note, however, that the transient-eddy contribution is predominantly negative. This is an unexpected result, since most studies of zonal-meanP−Echanges use in some way a scaling up of transient-eddy moisture fluxes by moisture changes (Held and Soden, 2006; Wu et al., 2011; Byrne and O’Gorman, 2015). Transient-eddy moisture fluxes (at least zonally anomalous ones) do not simply increase linearly with the surface specific humidity. This is perhaps not surprising given the dependence of transient-eddy fluxes on temperature gradients and thus moisture gradients (O’Gorman and Schneider, 2008b; Byrne and O’Gorman, 2015). Together, reductions of stationary- eddy vertical motions and transient-eddy moisture fluxes act to decrease rms(P∗−E∗) at all latitudes, but especially in the tropics.
So far, all figures and discussion have been of multi-model means. Given the spread in zonal- meanP−E(Voigt and Shaw, 2015), it would be surprising if the models agreed on the climatology of rms(P∗−E∗). We show the global-mean, tropical-mean, and extratropical-mean rms(P∗−E∗) for all models on the x-axis of Fig. 4.4. For comparison, we compute the climatology of rms(P∗−E∗) in ERA-Interim reanalysis for the period 1979–2012. Averages over the same latitude bands are shown as orange stars in Fig. 4.4. The spread in rms(P∗−E∗) is large. The ERA-Interim value is in the upper end of the range in the tropics and global mean and far beyond the upper end of the range in the extratropics. CMIP5 models are not simulating enough zonal variability in midlatitudeP−E.
0.6 0.65 0.7 0.75 0.8
−0.1
−0.05 0 0.05 0.1 0.15
rms(P*−E*) (m yr−1)
δ rms(P*−E*) (m yr−1 K−1) 0.4 0.42 0.44 0.46 0.48 0.5 0.520
20 40 60 80 100
rms(P*−E*) (m yr−1) δ rms(P*−E*) (m yr−1 K−1 )
δ rms(P*−E*) δRMSmthermo δRMSmdyn δRMStrans
ERA−Interim climatology 0.4 0.42 0.44 0.46 0.48 0.5 0.52
−0.05 0 0.05
rms(P*−E*) (m yr−1) δ rms(P*−E*) (m yr−1 K−1)
0.2 0.24 0.28 0.32
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rms(P*−E*) (m yr−1) δ rms(P*−E*) (m yr−1 K−1)
Global
Tropical 00.4 0.42 0.44 0.46 0.48Extratropical0.5 0.52
20 40 60 80 100
rms(P*−E*) (m yr−1) δ rms(P*−E*) (m yr−1 K−1 )
δ rms(P*−E*) δRMSmthermo δRMSmdyn δRMStrans
ERA−Interim climatology
Figure 4.4: Global-mean, tropical-mean (±0–30◦), and extratropical-mean (±30–75◦)δrms(P∗−E∗) plotted versus the PAST climatology of rms(P∗−E∗) for each model. The global average of the mean-thermodynamic, mean-dynamic, and transient contributions to this change are shown separately in blue, red, and purple dots. For comparison, the climatology of rms(P∗−E∗) in ERA-Interim reanalysis for the period 1979-2012 is shown with an orange star.
The y-axis in Fig. 4.4 shows the change in rms(P∗ −E∗) per degree of warming (computed locally) in these latitude bands, as well as the full thermodynamic, dynamic, and transient-eddy components. Spread in rms(P∗−E∗) is large, but several aspects of the change are robust. All models except 1 (GFDL-ESM2G) show an increase in global-mean rms(P∗−E∗) with warming. All models have an increase that is less than the expectation from thermodynamics alone. The majority of models show a larger change coming from stationary-eddy than transient-eddy dynamic changes.
Note also that the thermodynamic contribution is generally larger than 7% K−1 (shown as a blue dotted line). This arrises from the difference between the simple- and mean-thermodynamic terms as well as the nonlinearity of changes.