Abruptmonsoontransitionsasseeninpaleorecords
can be explained by moisture-advection feedback
Anders Levermanna,b,c,1, Vladimir Petoukhova, Jacob Schewea, and Hans Joachim Schellnhubera,d
Abrupt Monsoon Transitions Exist in
Paleorecords and Pertinent Models
continuity, and zero boundary conditions for vertical
velocity at surface and tropopause, yields
Paleoclimatic records show abrupt monsoon shifts at
various different locations and historic periods (1–5). An
important question is whether such transitions are possible in the future (6). To this end, we carved out the
physical mechanism for such transitions in a purposefully
simple conceptual model (7). Recently, Boos and
Storelvmo (8) claimed that introducing adiabatic cooling
into our model (7) eliminates these abrupt transitions.
This claim is not generally true. As can be seen from their
figure 1, Boos and Storelvmo (8) only eliminate abrupt
transitions if most of the energy from the rain’s latent
heat release is consumed by adiabatic cooling. Although
adiabatic cooling exists and is, as shown below, implicitly accounted for in ref. 7, it is not a valid assumption
that most of the latent heat release is consumed by this
process. By contrast, monsoon circulation is predominantly sustained by latent heat release, as shown in a
number of studies (e.g., ref. 9) including figure 2 in ref. 7.
Adiabatic Cooling Is Present in Our Model
Boos and Storelvmo (8) used a very specific linearized
representation of adiabatic cooling based on an approximation of the second horizontal derivative of
temperature by a linear function of its first horizontal
derivative, dividing velocity scale and length scale
(their equations 1−3, S1, and S2). This approximation
is crude. Here we show that our model (7) implicitly
incorporates adiabatic cooling without eliminating the
possibility of abrupt monsoon transitions as have been
reported from paleorecords.
Our model (7) is based on the entropy equation
ds QV
,
ρ =
dt T
[1]
with s = cp ln ϑ, cp, and ϑ being specific entropy, specific heat, and potential temperature of air, respectively. QV is the net heating rate per volume, and T
is kinetic temperature. Vertical integration from Earth’s
surface to the tropopause, ztr, and horizontally over the
monsoon land region Σ, assuming quasi-stationarity,
cp
Z !Z
X
ztr
0
"
Z !Z
∇H · ρϑ~
V H dz dσ =
X
+
ztr
0
Z !Z
X
"
ϑ
QV ,P dz dσ
T
ztr
0
"
ϑ
QV ,R dz dσ,
T
[2]
where H denotes the horizontal plane. QV ,P and
QV ,R are the net heating rate per unit volume due
to the condensation/precipitation and radiation, respectively. In our simple model, we neglected the
sensible heat flux at the land surface. The precipitation heating is nonnegative and the radiation heating is nonpositive throughout the entire troposphere
in the continental monsoon regions (10).
The deviation of the positive factor ϑ=T from 1 quantifies the contribution of vertical motions to the atmospheric heat balance, i.e., in the adiabatic atmosphere
(T = ϑ) vertical motions cannot contribute to the heat
balance. Bringing ϑ=T out of the integrals in Eq. 2, one
obtains an equation with identical structure to equation
1 of ref. 7,
LPSP − « cp W ΔT + RSR = 0,
[3]
where SP and SR are integral precipitation- and radiationdriven stability parameters. Using the same notation and
definitions as in both models (7, 8), one then gets
W3 +
$
β 2 α #
αβ
W −
RSR = 0,
LSP β qO + RSR W − 2
«ρ
« c p
« ρ cp
[4]
which has the same general structure as the governing
equation 5 in ref. 7 showing the same abrupt transitions.
As a consequence, the threshold behavior is not eliminated by adiabatic cooling unless it consumes practically all
of the energy of the latent heat release. However, the latter
assumption is supported neither by record nor by theory.
a
Potsdam Institute for Climate Impact Research, 14473 Potsdam, Germany; bLamont-Doherty Earth Observatory, Columbia University, New York,
NY 10964; cInstitute of Physics, Potsdam University, 14476 Potsdam, Germany; and dSanta Fe Institute, Santa Fe, NM 87501
Author contributions: A.L. and V.P. designed research; A.L. and V.P. performed research; J.S. and H.J.S. contributed new reagents/analytic tools;
and A.L. and V.P. wrote the paper.
The authors declare no conflict of interest.
1
To whom correspondence should be addressed. Email: Anders.levermann@pik-potsdam.de.
www.pnas.org/cgi/doi/10.1073/pnas.1603130113
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LETTER
LETTER
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