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Dry and moist dynamics shape regional patternsof extreme
precipitation sensitivityJi Niea,1 , Panxi Daia,1, and Adam H.
Sobelb
aDepartment of Atmospheric and Oceanic Sciences, Peking
University, Beijing 100871, China; and bDepartment of Applied
Physics and AppliedMathematics, Columbia University, New York, NY
10027
Edited by Kerry A. Emanuel, Massachusetts Institute of
Technology, Cambridge, MA, and approved March 9, 2020 (received for
review August 6, 2019)
Responses of extreme precipitation to global warming are ofgreat
importance to society and ecosystems. Although observa-tions and
climate projections indicate a general intensification ofextreme
precipitation with warming on global scale, there are sig-nificant
variations on the regional scale, mainly due to changes inthe
vertical motion associated with extreme precipitation. Here,we
apply quasigeostrophic diagnostics on climate-model simula-tions to
understand the changes in vertical motion, quantifyingthe roles of
dry (large-scale adiabatic flow) and moist (small-scaleconvection)
dynamics in shaping the regional patterns of extremeprecipitation
sensitivity (EPS). The dry component weakens in thesubtropics but
strengthens in the middle and high latitudes; themoist component
accounts for the positive centers of EPS inthe low latitudes and
also contributes to the negative centers inthe subtropics. A
theoretical model depicts a nonlinear relation-ship between the
diabatic heating feedback (α) and precipitablewater, indicating
high sensitivity of α (thus, EPS) over climatologi-cal moist
regions. The model also captures the change of α due tocompeting
effects of increases in precipitable water and dry staticstability
under global warming. Thus, the dry/moist decomposi-tion provides a
quantitive and intuitive explanation of the mainregional features
of EPS.
precipitation extreme | convection | climate change
A warmer climate has more water vapor, which tends to inten-sify
extreme precipitation events in general. Observationaltrends and
climate simulations indicate this intensification on aglobal scale
(1–6), but regional responses of extreme precipita-tion exhibit
wide geographic variation (3–8). Regional patternsof extreme
precipitation sensitivity (EPS) (defined here as thefractional
change in extreme precipitation per degree of globalwarming) can be
separated into a relatively homogeneous ther-modynamic component
representing changes in water vapor(which approximately follows the
Clausius–Clapeyron [CC] scal-ing, 7%/K), and a dynamic component
representing changesin vertical motion. The dynamic component
contributes mostof the regional variation in EPS (8). Thus, the key
to under-standing the regional patterns of EPS is to understand
thechanges of vertical motion in extreme precipitation events.This
is a subtle task, because vertical motion and precipi-tation are
closely coupled, making cause and effect difficultto untangle.
The dynamics that control vertical motion vary with latitude,due
to variations in the Coriolis effect. In the deep tropics, ascentis
closely associated with latent heating of moist convection (9,10).
In the extratropics, vertical motion is also strongly con-strained
by quasibalanced dynamical processes associated withthe potential
vorticity field, represented most simply by quasi-geostrophic (QG)
dynamics. Extratropical extreme precipitationevents are usually
associated with large-scale perturbations suchas fronts and
cyclones (11, 12). A given large-scale perturba-tion induces
dynamically forced vertical motion, and would doso even in a dry
atmosphere. In the real, moist atmosphere, itstimulates the
development of moist convection by destabilizingthe atmospheric
stratification. The latent heating then released
by the convection, in turn, drives further large-scale ascent.
Boththe dry adiabatic dynamics due to the large-scale
perturbationsand the diabatic heating due to the moist convection
are impor-tant in generating vertical motion in extreme
precipitation events(13, 14). Thus, it is useful to view extreme
precipitation as a sys-tem consisting of forcing (by large-scale
adiabatic perturbations)and feedback (by diabatic heating).
Here, we apply QG diagnostics to understand the regional
pat-terns of EPS in climate projections from the Coupled
ModelIntercomparison Project Phase 5 (CMIP5). The QGω equation
isused to decompose the vertical pressure velocity (ω) in
extremeprecipitation (excluding the deep tropics, where QG is not
valid)into a part (ωD ) due to large-scale adiabatic forcings (F )
anda part (ωQ ) due to diabatic heating (Q), respectively
(Meth-ods). With the previous proposed extreme precipitation
scalingusing vertical velocity (4), extreme precipitation (P) may
beexpressed as P =PD +PQ =PD(1+α), where PD and PQ arethe
precipitation corresponding to ωD and ωQ , respectively, andα=
PQPD
is a parameter measuring the diabatic heating feedbackassociated
with moist convection. The above equation separatesprecipitation
into a dry component (PD ) corresponding to theadiabatic dynamic
forcing by large-scale perturbations and amoist component (α)
representing the diabatic-heating feedbackassociated with moist
convection. The dry/moist decompositionmay also be thought as an
adiabatic/diabatic decomposition.
Significance
The factors controlling the large regional variations in
sim-ulated responses of extreme precipitation to global warm-ing
are poorly understood. Standard diagnostics break theresponses into
thermodynamic and dynamic componentsassociated with moisture and
vertical motion. The verticalmotion is the more poorly understood;
we use a methodto understand it by decomposing it into dry and
moistcomponents. The moist component can be predicted by asimple
model that explains how dynamics and thermody-namics are coupled.
This allows us to explain the regionalvariations in vertical
motion, and thus extreme precipitation,in terms of the dry
quasigeostrophic forcing and moisture,a deeper level of explanation
than is available from thethermodynamic–dynamic decomposition on
its own.
Author contributions: J.N. and A.H.S. designed research; J.N.
and P.D. performedresearch; J.N. contributed new reagents/analytic
tools; P.D. analyzed data; and J.N., P.D.,and A.H.S. wrote the
paper.y
The authors declare no competing interest.y
This article is a PNAS Direct Submission.y
Published under the PNAS license.y
Data deposition: The CMIP5 data archive is available at
https://esgf.llnl.gov. The analysisand codes are available at
https://www.jiniepku.com/download.html.y1 To whom correspondence
may be addressed. Email: [email protected] or [email protected]
This article contains supporting information online at
https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1913584117/-/DCSupplemental.y
First published April 6, 2020.
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Correspondingly, the dry/moist decomposition can be applied
tothe EPS (δ lnP):
δ lnP = δ lnPD + δ ln(1+α), [1]
where δ lnPD includes changes in both water vapor and ωD ,and δ
ln(1+α) represents changes of the diabatic-heating feed-back (15).
We will show that the dry and moist componentstogether shape the
regional patterns of EPS in climate projec-tions and provide
insights into the behavior of each component,as described
schematically in Fig. 1.
MethodsDaily data from 20 models in the CMIP5 archive (SI
Appendix, Table S1)are used in this study. The present climate is
represented by the his-torical simulations between 1981 and 2000,
and the warmer climate isrepresented by the RCP8.5 scenario
simulations between 2081 and 2100.The climatic response of a
quantity is calculated as fractional changes(denoted by δ ln)
between these two periods normalized by the global-mean surface
warming. Since we are interested in regional-scale
extremeprecipitation in this study, extreme precipitation (denoted
by P) of eachgeographic location is defined as the annual maximum
daily precipitationover a surrounding 7.5◦× 7.5◦ regional box. At
each location, diagnosesare performed on the extreme precipitation
day of each year. Then, wecompose all of the events during each
20-y period and apply multimodelaveraging. The size of the regional
box is chosen since it better suits theQGω inversion (16). We
verified the sensitivity of our results to the def-inition of
extreme precipitation by using 3.75◦× 3.75◦ regional boxes.Changing
to smaller regional boxes leads to larger climatological
precip-itation amounts; however, the EPS and its decomposition are
very closeto those shown here (comparing Figs. 2 and 3 with SI
Appendix, Figs. S11and S12).
The QGω diagnostics follows similar methods as those of refs. 13
and14. It calculates the linear inversion of the QGω equation to
assess contribu-
Fig. 1. A proposed roadmap for understanding the EPS. The
thermody-namic/dynamic decomposition (8) (light gray boxes) show
that the changesof vertical motion account for most regional
features, however, with causesunsolved. This study (dark gray
boxes) further applies a dry/moist decom-position of vertical
motion into parts due to large-scale adiabatic forcingsand
diabatic-heating feedback. Diagnoses from climate model outputs
anda simple model link the changes in the diabatic-heating feedback
to thechanges in local atmospheric moisture and the dry static
stability. Futurestudies (dashed-line arrows) should link the
changes of F to the changesof large-scale background conditioned on
extreme precipitation or, evenfurther, to the changes of mean
states.
tions of vertical motion from different physical processes. The
QGω equationreads
(∂pp +σ
f2∇2)ω=−
1
f∂pAdvζ −
R
pf2∇2AdvT −
R
pf2∇2Q, [2]
where σ=− RTp ∂p ln θ is the dry static stability, and f is the
Coriolis parame-ter. Advζ =− ~Vg · ∇ζ and AdvT =− ~Vg · ∇T are the
horizontal advection ofgeostrophic absolute vorticity (ζ) and
temperature (T) by geostrophic winds,respectively. The sum of first
two right-hand-side (RHS) terms in Eq. 2 is thedry adiabatic
dynamic forcings (F) (the dry part), and the third RHS term isthe
diabatic heating term (the moist part). Taking advantage of the
linear-ity of the QGω equation, we solve Eq. 2 on the
three-dimensional sphericalgrids including the RHS terms one by one
(detailed in SI Appendix, sectionS1). Thus, we have the
decomposition ω=ωD +ωQ, in which ωD correspondsto the dry adiabatic
dynamic forcings (F), and ωQ corresponds to the diabaticheating
term (the third RHS term). ω is then converted to precipitation
bythe scaling proposed in ref. 4.
Since the CMIP5 models do not provide the diabatic heating (Q),
wemay calculate it as the residual term in the temperature budget
equation(13) and then use it to solve ωQ, Or we may calculate ωQ as
the residualterm with other components of ω calculated by directly
solving the QGωequation. ωQ calculated by the two methods are
reasonably close to eachother (SI Appendix, Fig. S2). The results
presented here are with ωQ cal-culated as the residual in the ω
equation; the main conclusions are notaffected by choice of methods
of calculating ωQ (validation in SI Appendix,section S1).
ResultsFirst, we examine the dry and moist components of extreme
pre-cipitation in historical simulations. The extreme
precipitationclimatology (Fig. 2A) has a geographic distribution
resemblingthat of the mean precipitation but with much greater
intensity.P in Fig. 2A is smaller than previous studies (e.g.,
figure 1 inref. 8) because, here, the precipitation extremes are
averagedover larger areas. P from direct model outputs is well
repro-duced by the scaling using vertical motion (8) (SI
Appendix,Fig. S7). The distribution of P shows an overall decrease
withlatitude, since water vapor is mostly confined to the low
lati-tudes. In contrast, the component of precipitation due to
drydynamical forcing (PD ) (Fig. 2B) peaks in the middle
latitudes,being approximately collocated with the storm tracks in
bothhemispheres. The strong meridional gradient of temperaturein
the midlatitudes leads to baroclinic instability and
activelygenerates synoptic storms. These midlatitude storms are
veryrobust features even in dry climate models without water
vapor(17, 18), indicating the essential role of dry QG dynamics.
Thelarge-scale dry perturbations are much weaker in the low
lati-tudes due to the weaker Coriolis effect, resulting in small
PDthere. Precipitation due to diabatic heating (PQ ) (Fig 2C) hasa
greater contribution to P than PD has, particularly in the
lowlatitudes where the abundant water vapor supports strong
con-vection. In the extratropics, the distributions of PD and PQ
areclosely related; the local maxima of PQ are roughly equator-ward
of the local maxima of PD (such as the northern hemi-sphere Pacific
and Atlantic storm tracks and the South PacificConvergence
Zone).
The close coupling between PD and PQ is quantified bythe
diabatic-heating feedback α (Fig 2D). α decreases withlatitude,
reflecting the shift in the dominant dynamics respon-sible for
generating vertical motion from convective heating inlow latitudes
to large-scale dry dynamics in higher latitudes.In addition, α
shows longitudinal variations that significantlycontribute to the
heterogeneity of P . Along the same longi-tude, α over the western
parts of the oceans is much greaterthan α over either the eastern
parts of the oceans or land.Interestingly, the geographic
distribution of α is highly corre-lated with water vapor abundance
(i.e., precipitable water H ,the white contours in Fig. 2D),
indicating the dominant role of
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Fig. 2. The decomposition of extreme precipitation from
historical simulations [P = PD + PQ = PD(1 +α)]. (A–D) The
multimodel mean of annual maximumdaily precipitation (P) (A); PD,
component due to dry forcing (B); PQ, component due to diabatic
heating (C); and diabatic heating feedback (α, color) (D).The white
contours (intervals of 10 mm) in D show the precipitable water (H)
conditioned on extreme precipitation day. The domain of maps (here
andbelow) is 75◦S ∼ 75◦N. QG diagnosis are masked within 5◦S ∼ 5◦N,
where the QG inversion is not applicable.
moisture in determining the responses of convection to
large-scale perturbations (19).
Inspired by the strong correlation between α and H , wedeveloped
a theoretical model of α capturing the essentialdynamics. The model
simplifies the structure of large-scaledynamics, while highlighting
the dependence of convection onlocal thermodynamic conditions. It
uses a reduced static sta-bility (σe) (9, 20, 21) to link
precipitation and the effects ofthe associated diabatic heating.
Assuming that a large-scaledisturbance associated with extreme
precipitation has a charac-teristic horizontal length scale with
corresponding wave numberk (which can be location-dependent), the
QGω equation may berewritten as
(∂pp −σek2
f 2)ω=F . [3]
We further assume the vertical structures of F , Q , and ω may
beapproximated by a single mode. We then obtain a simple formulafor
α (detailed derivation in SI Appendix, section S2):
α=bH
1− bH . [4]
The coefficient b is inversely proportional to the dry static
sta-bility (σ) and proportional to the ratio of the disturbance
lengthscale to the Rossby radius of deformation (discussion of the
roleof this length scale is in refs. 22 and 23). The scatter plot
of α andH from climate-model outputs fits the theoretical curve
obtainedfrom Eq. 4 well, even with a horizontally uniform b (Fig.
4A).
The map of α provided by Eq. 4 with the fitted b=0.017 mm−1
also matches that from QG diagnostics (SI Appendix, Fig. S8
andFig. 2D) reasonably well. The simple model also provides a
the-oretical formula of b, which predicts b in the same order of
mag-nitude as the diagnosed b but with uncertainties in the choices
ofparameters (discussion in SI Appendix, section S2). The
factorsthat could potentially lead to substantial geographic
variations inb largely cancel, resulting in a nearly horizontally
uniform b thatabsorbs all of the complexity in convective
responses. The non-linear relationship in Eq. 4 quantifies the
rapid intensificationof the diabatic heating feedback (thus,
precipitation extremes)with increasing moisture. Nonlinear
relationships between pre-cipitation and moisture have been found
in other contexts withdifferent formulas (24, 25); the present
context differs in thatα is not the total precipitation but the
diabatic response todry adiabatic forcing. The simple model works
not only for themultimodel mean but also for individual models (SI
Appendix,Fig. S4); the intermodel spread in α (SI Appendix, Fig.
S4)is presumably mainly due to differences in model
convectiveparameterizations (26).
We now consider the simulated responses of extreme
precipi-tation to climate change. The EPS from model outputs (Fig.
3A)shows distinct regional patterns similar to those found in
pre-vious studies (6, 8). The EPS is positive in most regions,
withmaxima in the equatorial Pacific, South Asian monsoon, andpolar
regions. It is negative in several regions over the sub-tropical
oceans to the west of continents. The EPS calculatedby the scaling
of ω (Fig. 3B) again reproduces that from direct
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Fig. 3. The EPS and its dry/moist decomposition [δ ln P = δ ln
PD + δ ln(1 +α)]. (A–D) The EPS (A), EPS approximated by the
scaling using ω (B), the drycomponent of EPS (δ ln PD) (C), and the
moist component [δ ln(1 +α)] (D). In E and F, δ ln PD is further
separated into the thermodynamic contribution (keepωD constant in
the scaling) and the dynamic contribution (full scaling minus
thermodynamic contribution). Stippling indicates that over 70% of
the modelsagree on the sign of the change.
model outputs well. Applying the dry/moist decomposition ofEPS
with Eq. 1 shows that the dry component (δ lnPD ) (Fig. 3C)accounts
for most of the positive values in the middle andhigh latitudes. δ
lnPD is weakly positive or even negative inthe low latitudes. In
contrast, the moist component [δ ln(1+α)] (Fig. 3D) is only weakly
positive in the middle and highlatitudes. It contributes to the
negative centers in the sub-tropics and accounts for the regions of
super-CC sensitivity inlow latitudes.
The dry component of EPS (δ lnPD ) includes changes ofwater
vapor—inasmuch as those cause changes in precipita-
tion for a fixed vertical velocity, that is, it excludes the
diabaticfeedback—and changes of ωD with warming. The thermody-namic
contribution, calculated as changes of precipitation usingthe
scaling without changing ωD , increases pervasively, with
arelatively homogeneous spatial distribution (8) (Fig. 3E).
Thedynamic component—the rest of δ lnPD excluding the
ther-modynamic component—is negative in most subtropical
andmidlatitude regions, particularly over the northern
subtropicalAtlantic Ocean (Fig. 3F). Changes in both the amplitude
(quan-tified as ωD at 500 hPa) and vertical shape of ωD contribute
tothe dynamic component (15); the former makes the dominant
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Fig. 4. Understanding the moist component of EPS [δ ln(1 +α)].
(A) Scatter plot of α and H for each geographic grid. Red is for
the historical period, andblue is for the warmer period. The solid
lines are the best-fit lines denoted by the equations in the
legends. The subtitle indicates correlation (R) between αand H, and
rmsd of α between model outputs and the theoretical lines for the
historical runs. (B) Map of the reconstructed δ ln(1 +α) using Eq.
4 with thefitted b in A. For demonstration, changes of α in two
representative regions (black rectangles) are marked as arrows in
A. The starting and ending pointsof the arrows correspond to the
historical and the warmer period, respectively. The dashed-line
arrow is with α from model diagnoses, and the solid-linearrow is
with α estimated using Eq. 4.
contribution, as indicated by a comparison between the changein
500 hPa ωD (SI Appendix, Fig. S9 and Fig. 3F). Changes in
thevertical shape of ωD make a sizable contribution only in high
lat-itudes. The changes in ωD are mostly due to the changes of
drydynamic forcing F (SI Appendix, Fig. S9). The systematic
weak-ening of ωD and F in lower latitudes and strengthening in
higherlatitudes are likely due to changes in the large-scale
circulation,which modifies the atmospheric baroclinicity and
propagationof disturbances (27–30). Further studies are needed to
link thechanges of dynamic forcing (F ) to general circulation
changes,such as Hadley cell expansion (31) and poleward shifts of
thestorm tracks (32).
Next, we examine the moist component of EPS [δ ln(1+α)].As
indicated by both direct diagnosis of the CMIP5 model outputand the
simple model (Fig. 4A and Eq. 4), the diabatic heatingfeedback (α)
nonlinearly depends on atmospheric moisture, asdoes its change:
δ ln(1+α)=α(δ lnH + δ ln b). [5]
Global warming increases both H and σ (since the tempera-ture
profile roughly follows a moist adiabatic lapse rate,
whichdecreases with warming) with opposite effects on α (SI
Appendix,Fig. S10). The increases of H amplify α by increasing
diabaticheating associated with condensation (33), while the
increasesof σ decrease α by inhibiting convection. A curve fit to
thediagnosed α (Fig. 4A) shows that δ ln b≈−6.5%, which is
consis-tent with the changes of σ (δ ln b≈−δ lnσ, neglecting
changesof Lh). The competing effects of increased H and b
deter-mine the sign of the local α changes. More importantly,
thetotal effect of δ lnH + δ ln b is amplified by the
climatologi-cal α (Eq. 5). In regions with large climatological
α—such asthe low latitudes and monsoon regions (Fig. 2D)—the
changesin the moist component (Fig. 3D) are much greater than inthe
regions with small climatological α. Reconstructions ofδ ln(1+α)
using H from model outputs and the fitted constant
b approximately reproduce its regional patterns as found fromthe
direct calculations (Figs. 3D and 4B). The negative centersin the
subtropics and the positive maxima in the tropical Pacificand South
Asia Monsoon region are captured by the simplemodel, albeit with
some discrepancies such as the underesti-mation of the subtropical
negative centers. The simple modelindicates that the diabatic
heating feedback and its response towarming are largely explained
by the local convective thermody-namic conditions, and independent
of the large-scale forcing (drydynamics), lending further support
to our dry/moist dynamicsdecomposition.
Lastly, we provide a zonally averaged view of the
dry/moistdecomposition of EPS (Fig. 5). The dry component (blue
line),while it dominates the EPS in the high latitudes, decreases
to val-ues close to zero in the low latitudes. This latitudinal
dependence
Fig. 5. A zonally averaged view of the dry/moist decomposition
of EPS.The black solid line is EPS from model outputs, and the
black dashed lineis EPS approximated by the scaling using ω. The
blue (red) solid line is thedry (moist) component of EPS. The red
dashed line is the moist componentcalculated using the fitted Eq.
4.
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is partly due to the latitudinal distribution of the
thermody-namic component (Fig. 3E, higher values in high latitudes
relatedto polar amplification) (34) and partly due to the
substantialweakening of dynamic forcing in the low latitudes (Fig.
3F). Onthe contrary, the moist component (red line) increases
sharplyas latitude decreases into the tropics. Again, the simple
model(red dashed line) captures the latitudinal dependence
reason-ably well; the discrepancies that remain may be alleviated
byallowing latitude-dependent parameters. The blue and red
linesintersect in the subtropics, corresponding to the local
minimumof EPS. The nonlinear relationship between α and
moisture(Eq. 5) indicates a large amplification of the diabatic
heat-ing feedback under warming in climatologically moist
regions,providing a simple explanation for the super-CC sensitivity
atlow latitudes.
Conclusions and DiscussionThis study applies a dry/moist dynamic
decomposition onextreme precipitation on a near-global scale to
understand theregional patterns of extreme precipitation
sensitivity from theCMIP5 simulations (schematic in Fig. 1). The
dry component(δ lnPD ) represents changes of precipitation due to
changesin QG forcing and atmospheric moisture (but without
con-sidering how the changes in moisture affect the
large-scalevertical motion). It shows weakening in the subtropics
andstrengthening in the middle-high latitudes with warming.
Futurestudies may further link this latitudinal pattern to changes
inthe general circulation. Model simulations with idealized
con-figurations (35) or even only dry atmospheres (18) could begood
starting points and provide insights for understandingthe
comprehensive climate simulations. The moist component[δ ln(1+α)]
represents the changes of diabatic-heating feed-back due to
convection. A simple model of the diabatic heat-ing feedback
captures the geographic distribution of α andits changes in model
simulations and shows the competingeffects of increased water vapor
and dry static stability. Thenonlinear dependence of convective
responses on moisture,depicted by the simple model, greatly
enhances the regionalheterogeneity by amplifying sensitivity over
climatologicallymoist regions.
There are some limitations of this study, which may beremedied
in future work. The dry/moist decomposition basedon QG theory works
reasonably well for regional-scale pre-cipitation extremes.
However, for extreme precipitation onsmaller scales, where the QG
approximation is poor, otherfactors, such as mesoscale organization
(36), may play impor-tant roles. Unlike previous analyses that
emphasized the roleof changes in the horizontal length scale of
precipitating dis-turbances (23), the results here suggest that
changes in lengthscale play only a secondary role. Nevertheless,
relaxing approx-imations in our simple model to include either
multiple hor-izontal length scales or multiple vertical modes will
allowmore detailed analyses of the mechanisms of regional EPS.In
addition, examining the characteristics of the cyclones pro-ducing
precipitation extremes and their changes with climate(29, 30, 37)
will provide a synergistic understanding of theconclusions
here.
The dry/moist decomposition can be used to gain under-standing
of other aspects of extreme precipitation variationsbesides their
long-term responses to forced climate change. Forinstance, does dry
or moist dynamics contribute more to theinterannual variation of
extreme precipitation? How does large-scale variability—e.g., the
El Niño/Southern Oscillation (38) andthe Annual Modes (39)—affect
extreme precipitation, throughmodulating the large-scale
disturbances or local thermodynamicconditions? Examining the
intermodel spread of dry and moistcomponents and comparing with
reanalysis may help identifykey factors leading to the biases and
guide further improve-ment of climate models; for example,
correcting the sensitivityof parameterized convection on
thermodynamic conditions (26)may reduce the biases in the moist
component and improve thesimulation of extreme precipitation.
Data Availability. The CMIP5 data archive is available at
https://esgf.llnl.gov. The analysis and codes are available at
https://www.jiniepku.com/download.html.
ACKNOWLEDGMENTS. We thank Paul O’Gorman, Ziwei Li, and Martin
Singhfor discussions; Neil Tandon for sharing part of the CMIP5
data; and twoanonymous reviewers for their valuable review. This
research was supportedby National Natural Science Foundation of
China Grant 41875050.
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