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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: jinie@pku.edu.cn or pancy@pku.edu.cn.y

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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