Andrew Hoell (U. Mass. 2011)Roop Saini (U. Mass. 2012)

Laurie Agel (U. Mass. 2018)

Argyro Kavvada (U. Maryland 2014*)

Joowan Kim (McGill, 2014)Patrick Martineau (McGill, 2015)

Jinqiang Chen (Caltech, 2015)Anna Laraia (Caltech, 2016)

Jennifer Walker (Caltech, 2017)Ho-Hsuan Wei (Caltech, 2018)

Huang Yang (Cornell 2015)Alex Burrows (Cornell 2017)

Yen-Ting Hwang (U. Washington 2013)Jack Scheff (U. Washington 2014)

Elizabeth Maroon (U. Washington 2016)

Nir Krakauer (Caltech 2006*)Simona Bordoni (UCLA 2007*)

Gretchen Keppel-Aleks (Caltech 2011*)Tim Merlis (Caltech 2011)

Alejandro Soto (Caltech 2012*)Xavier Levine (Caltech 2013)

Cheikh Mbengue (Caltech 2015)Zhihong Tan (Caltech 2016)Robert Wills (Caltech 2016)

Tobias Bischoff (Caltech 2017)Bettina Meyer (ETH Zurich 2017)

Xiyue Zhang (Caltech 2018)

Juliana Dias (NYU, 2010)

Frédéric Laliberté (NYU, 2011)Ray Yamada (NYU, 2016)

Luca Autieri (Bologna, 2013*)Elena Scardovi (Bologna, 2015*)

Benjamin Cash (Penn State 2001)Hyun-kyung Kim (Penn State 2001)

Seok-Woo Son (Penn State 2006)Adam Edson (Penn State 2008)

Jacob Haqq-Misra (Penn State 2010)Changyun Yoo (Penn State 2011)

Cory Baggett (Penn State 2016)Qian Li (Penn State 2018)

Salil Mahajan (Texas A&M 2009)Xiaojie Zhu (Texas A&M 2013)

Jesse Steinweg-Woods (Texas A&M 2016)Tarun Verma (Texas A&M 2017)

Chul Eddy Chung (U. Maryland 1999)Ying Dai (U. Maryland 1999)

Mathew Barlow (U. Maryland 1999*)Eric DeWeaver (U. Maryland 1999)

Alfredo Ruiz-Barradas (U. Maryland 2001*)

Scott Weaver (U. Maryland 2007)Steven Chan (U. Maryland 2008)

Megan Linkin (U. Maryland 2008)Ching-Yee Chang (U. Maryland 2008*)Bin Guan (U. Maryland 2008) Massimo Bollasina (U. Maryland 2010)Kye-Hwan Kim (U. Maryland 2013)Argyro Kavvada (U. Maryland 2014*)Yongjing Zhao (U. Maryland 2014*)Stephen Baxter (U. Maryland 2016)Ni Dai (U. Maryland 2018*)Natalie Thomas (U. Maryland 2018)

Jia-yuh Yu (UCLA 1994)Chia Chou (UCLA 1997)Hsin-Hsin Syu (UCLA 1997)Wenjie Weng (UCLA 1998)Mark Roulston (Caltech 2000) Johnny W.-B. Lin (UCLA 2000)Katrina Hales (UCLA 2005)Chris Holloway (UCLA 2009)

Diana Bernstein (HUJI 2014)Baird Langenbrunner (UCLA 2015)

Xuan Ji (UCLA 2016)Kevin Quinn (UCLA 2017)

Kathleen Schiro (UCLA 2017)Yi-Hung Kuo (UCLA 2019)

Frédéric Vitart (Princeton 1998)Shree Khare (Princeton 2005)

Hui Wang (U of Illinois at Urbana-Champaign 1997)

Hailan Wang (UIUC 2000)Lourdes Aviles (UIUC 2004)

Stefan Sobolowski (Columbia 2010)Yutian Wu (Columbia 2011)

Colin Kelley (Columbia 2014)Xiaoqiong Sage Li (Columbia 2018)

*This PhD was co-advised by an additional mentor

R. SaravananPrinceton 1990

Dargan FriersonPrinceton 2005

Sukyoung LeePrinceton 1991

Tapio SchneiderPrinceton 2001

Olivier PauluisPrinceton 2000

Yunqing ZhangPrinceton 1997

Jiawei ZhangPrinceton 1995

Valentina PavanPrinceton 1994

Xin TaoPrinceton 1991

Erica StaehlingPrinceton 2014

Sarah KangPrinceton 2009

Gang ChenPrinceton 2007

Mingfang TingPrinceton 1990

Jeffrey AndersonPrinceton 1990

Jean-Paul M. HuotPrinceton 1988

David NeelinPrinceton 1987

Sumant NigamPrinceton 1984

Prashant D. Sardesh-mukh Princeton 1983

Wenyu ZhouPrinceton 2015

Andrew BallingerPrinceton 2015

Todd MooringPrinceton 2016

Junyi ChaiPrinceton 2016

Chiung-Yin ChangPrinceton (in progress)

Nicholas LutskoPrinceton 2017

Isaac HeldPrinceton 1976

Eric DeWeaver

Mathew Barlow Steven Chan

Natalie Thomas

Andrew Ballinger

Tobias Bischoff Simona Bordoni

Gang Chen

Juliana Dias

shown), which is not surprising with a radiation schemethat does not contain cloud– or water vapor–radiativefeedbacks. The other forcing in the moist static energyequation, the sensible heat flux, is relatively small andcorrelated with the evaporation. Frictional convergenceacts to power the waves as well, but the moisture con-verged in the boundary layer by this feedback is ap-proximately 4 times smaller than the evaporation dif-ferences (not shown).

The evaporation maximum leading the precipitationis caused by larger wind speeds near the surface on theeastern side of the wave, in accordance with the evapo-ration–wind feedback theory (Neelin et al. 1987; Eman-uel 1987). The mean surface easterlies at the equatorfor this simulation are approximately 2.7 m s�1, andwhen surface convergence is superimposed upon thismean wind, the zonal winds vary significantly across thewave (between 0 and 6 m s�1; Fig. 4c). Since the windsare primarily zonal in this region, and since evaporationis proportional to the surface wind, this leads to thevariation of evaporation following the structure of thesurface zonal wind in Fig. 4.

To confirm the evaporation–wind feedback mecha-nism as the driver of these waves, we have altered theevaporation formulation to suppress the dependenceon wind speed by replacing this by a globally averagedvalue. In this simulation, the Kelvin wave was com-

pletely eliminated (not shown). Additional methods toreduce the effectiveness of the evaporation-wind feed-back mechanisms include introducing a large gustinessvelocity in the evaporation formulation, and reducingthe oceanic mixed layer depth to zero. Since evapora-tion–wind feedback strengthens eastward-propagatingwaves and weakens westward propagating waves, thisfeedback is a likely reason why there are no Rossbywaves or other westward-propagating waves in Fig. 1.While evaporation–wind feedback may contribute tothe growth of Kelvin waves in nature, this theory doesnot fully explain observed Kelvin waves such as those inWheeler et al. (2000).

We next focus on the vertical structure of the wavesalong the equator, starting with the pressure velocityand the specific humidity, shown in Fig. 5. The maxi-mum vertical velocity is in the midtroposphere; how-ever, some higher-mode vertical structure can be seenhere as well. Shallow convection leads the maximumprecipitation, as seen in observations. Lower tropo-spheric moisture leads the convection, and is graduallypropagated upward by the shallow convection; this pre-conditions the troposphere for deep convection. Differ-ing from observations here is the lack of a stratiformcloud deck trailing the area of deep convection. It is notsurprising that this aspect of observations cannot becaptured in our model, which has no condensate. It is

FIG. 3. Control case Kelvin wave composite anomalies for (a) surface wind (m s�1) andprecipitation (W m�2), (b) midtropospheric pressure velocity (Pa s�1), and (c) surface pres-sure (Pa).

JUNE 2007 F R I E R S O N 2081

Fig 3 live 4/C

Dargan FriersonYen-Ting Hwang

fraction is reduced abruptly from 50% when RHSBM

approaches 90%, consistent with the asymmetry of pre-

cipitation response for these cases.

In the K08 study, the sensitivity of the ITCZ response

to physical parameters is related to changes in energy

flux and compensation. However, in the simulations

presented here, there is almost no change in energy flux:

we obtain about the same amount of C as RHSBM is

varied, as shown in Fig. 5. Therefore, a theory for the

different tropical precipitation responses in these cases

must be based on something other than the energy

budget.

4. Prediction of the tropical precipitationresponses

a. Energy balance model

As the first step to predict the tropical precipitation

response, we predict atmospheric energy fluxes from a

one-dimensional (in latitude) EBM in which all of the

energy transport is treated as a diffusion process (Sellers

1969) and impose the same oceanic heat fluxes H. A

diffusive model is not a good approximation for the

tropics but may be adequate for the extratropical fluxes

that, in the image described in section 3a, drive the

tropical energy transports. As in Frierson et al. (2007),

we diffuse moist static energy (m), and the form of the

energy balance model can be written as

SW�OLR1H5�~D

a2 cosu

›

›ucosu

›m

›u

� �, (3)

where SW is a prescribed solar radiation as in the ide-

alized moist GCM. Here, OLR is assumed to be a linear

function of the surface temperature (Ts in K), OLR 51.4Ts 2 156 (in W m22), which is the equation of the

least squares regression line obtained from the control

simplified moist GCM. The diffusion coefficient ~D is

related to the kinematic diffusivity D by ~D 5 ps D/g,

where ps/g 5 104 kg m22, the mean mass of an atmo-

spheric column per unit area. The value D 5 9.5 3105 m2 s21 is obtained from the idealized GCM by

averaging

�

1Dp

ð0

ps

my dp

1a›m

›u

����ps

���������

���������

FIG. 6. Schematic of the mechanism that determines C. The gray oval indicates the anom-

alous Hadley circulation, of which the direction is denoted with black arrows. The blue (red)

part of the arrow, which represents changes in atmospheric energy transports mostly by eddies

at the edge of the tropics and by the Hadley circulation within the tropics, indicates cooling

(warming). The clockwise anomalous Hadley circulation transports energy northward to cool

(warm) the southern (northern) subtropics where it is warmed (cooled) by eddies. Hence, the

compensation in the tropics is determined by the response of the total energy fluxes near the

edge of the tropics (;20–308N or S).

SEPTEMBER 2009 KANG ET AL . 2819Sarah Kang

Gretchen Keppel-Aleks

Frédéric Laliberté

Xavier LevineNicholas Lutsko

Bettina Meyer

Tim Merlis

Sumant Nigam

Olivier Pauluis Valentina Pavan

Luca Autieri

Xiaojie ZhuJesse Steinweg-Woods

Tarun Verma

R. Saravanan

Salil Mahajan

Prashant D. Sardeshmukh

2 T. Schneider and I. M. Held

a

! T

[Kel

vin]

January

-1

0

+1 c July

Year

b

Ampl

itude

1920 1950 1990 -2

0

+2

Year

d

1920 1950 1990

FIGURE 1: First discriminants of interdecadal variations in January (a, b) and July (c, d) temperatures. The discriminating patterns(a, c) and canonical variates (b, d) represent temperature changes relative to the 1916–1998 mean, local changes being productsof the canonical variate and the local values of the associated discriminating pattern. The discriminants are normalized such thatthe canonical variates have unit variance. In the amplitude time series (b, d), black lines indicate unfiltered canonical variates andred lines indicate low-pass filtered canonical variates. In the spatial pattern of temperature changes (a, c), white patches indicateregions excluded from the analysis because of insufficient data coverage; the red boxes in the July discriminating pattern (c) outlineregions for which mean temperatures are shown in Fig. 2a.

power, the discriminatory power being measured as theratio of among-group variance to within-group variance.In this study, the variables represent Earth surface tem-peratures at the nodes of a spatial grid, and data for ap-proximately one decade form a group. The first canoni-cal variate, discriminating among decadal data groups,is that linear combination of surface temperatures forwhich the ratio of interdecadal variance to intradecadalvariance is maximized. Higher-order canonical variatesmaximize this ratio subject to the constraint that they areuncorrelated with lower-order canonical variates. As-sociated with the canonical variates are discriminatingpatterns, spatial patterns that consist of the regressioncoefficients of the temperature data onto the canonicalvariates (see Appendix c). The value of a canonical vari-ate indicates, for any given time, the amplitude of theassociated discriminating pattern in the data. Thus, apair consisting of a discriminating pattern and a canon-ical variate, a pair we call a discriminant, characterizesinterdecadal temperature variations spatially and tempo-rally. In that the discriminant analysis extracts uncor-related discriminants with successively decreasing ratiosof interdecadal to intradecadal variance, it can be viewedas lifting off successive decoupled layers of interdecadalvariations from the temperature data.

3. Results

We identified discriminants of interdecadal variations inthe monthly mean surface temperatures for the years1916 through 1998 in the region between and

. In this period and region, data coverage is suf-ficiently continuous for a multivariate analysis (see Ap-pendix for details).Figure 1 shows the first discriminants for January and

July. (The first discriminants for the other months of thesolstice seasons have a similar structure.) Since temporalcorrelations within or among the decadal data groups arenot taken into account in the discriminant analysis, thefact that the time evolution of the first canonical variateis coherent over decades, for both January (Fig. 1b) andJuly (Fig. 1d), is evidence that the first discriminants arenot artifacts of the analysis but represent significant in-terdecadal temperature variations. For the first discrim-inants for January and July, the ratio of interdecadalto intradecadal variance is approximately .1 For com-parison, for the spatial mean temperatures in the periodand region analyzed, the variance ratio is for Jan-uary and for July. That is, the discriminant analy-sis separates interdecadal and intradecadal climate vari-ations much more efficiently than a spatial mean.The first discriminants are robust; their qualitative

features do not depend on analysis parameters such aschoice of data groups. The second and third canonicalvariates show time evolutions that are likewise coher-ent over decades, with variance ratios ; canoni-cal variates of yet higher order show no temporal coher-ence and variance ratios . The time evolutions ofthe higher-order canonical variates are non-monotonic,

1The variance ratio for the discriminants is to be interpreted cau-tiously, since it is biased to high values (see Appendix d). Hence, weonly quote approximate values.

Tapio Schneider

Geophysical Research Letters 10.1002/2016GL068418

Figure 1. Multimodel mean 1976–2005 climatology of (a) P− E and (b) P∗ − E∗ and change of (c) P− E and (d) P∗ − E∗ bythe end of the century (2070–2099) in the RCP8.5 scenario. (e and f) Thermodynamic contributions to Figures 1c and 1d,as estimated from the fractional change in surface specific humidity (equations (1) and (2)). Stippling indicates wherethe thermodynamic scaling is opposite in sign to the simulated change. (g) Zonal correlations of moisture budgetchanges with � (P∗ − E∗): thermodynamic, dynamic, and transient-eddy components based on the moisture budgetdecomposition in equation (3) (solid lines) as well as approximations to the thermodynamic and dynamic componentsbased on equations (2) and (9), respectively (dashed lines).

where u is the horizontal wind, q is the specific humidity, ()′ indicates the difference from the annual-meanclimatology, and ⟨⟩ denotes a mass-weighted vertical integral over the whole domain. The dynamic termhere combines the stationary-eddy components of the dynamic term and the nonlinear term of Seageret al. [2010], such that the decomposition is exact. The transient-eddy term is computed from a residual andincludes all temporal correlations between specific humidity and the horizontal wind, including seasonalcorrelations [cf. Wills and Schneider, 2015]. (The conclusions that follow are not substantially altered by theinclusion of seasonal correlations with the transient-eddy term; see the supporting information.)

Throughout the tropics, subtropics, and Southern Hemisphere midlatitudes, regional P∗ − E∗ changes areprimarily governed by changes in stationary-eddy circulations (red line in Figure 1g). Changes in zonallyanomalous transient-eddy moisture fluxes are negatively correlated with P∗ − E∗ changes in the tropics butplay a large role in the extratropical P∗ − E∗ change in both hemispheres. The thermodynamic term, onwhichthe simple thermodynamic scaling of equation (2) is based, is not well correlated with �(P∗ − E∗) (Figure 1g).Thus, to understand P∗− E∗ changes, one primarily has to understand stationary-eddy changes.

WILLS ET AL. CHANGES IN ZONAL P − E VARIANCE 4642

Robert Wills

Jack Scheff

Alejandro Soto

Zhihong Tan

FIG. 2. Domain mean profiles of (a) liquid ice potential temperature, (b) total water specific humidity, (c)

cloud liquid water specific humidity, and (d) the sum of cloud ice and snow water specific humidity. Black dotted

lines are the initial condition profiles. Gray shading shows the LES intercomparison range in Ovchinnikov et al.

(2014). The pink dots show the aircraft observations of flight 31 of ISDAC campaign on April 27, 2008. The

horizontal lines indicate the 15–85 percentile range for the measurements binned every 50 m.

827

828

829

830

831

44

Xiyue Zhang

Yungqing Zhang Frédéric VitartMingfang Ting

Yongjing Zhao

Stephen Baxter

Previous studies have shown a dependence of storm

track response on storm track latitude (Kidston and

Gerber 2010; Garfinkel et al. 2012). This result is qual-

itatively reproduced in our simulations varying convec-

tive stability (Fig. 4) and varying radiative equilibrium

temperatures (top right panel of Fig. 3): the storm

track’s poleward migration levels off at the highest lat-

itudes. Additionally, storm tracks shift little as the con-

vective stability is varied for g * 0.9; the reasons for this

are unclear.

All simulations show that the Hadley circulation

widens as the storm tracks migrate poleward (Figs. 3 and

4)—a correlation noted previously by Kang and Polvani

(2010) and Ceppi and Hartmann (2012). But Fig. 4

shows more particularly that storm tracks migrate in

tandemwith theHadley cell terminus when varying only

the tropical convective stability; however, the migration

is less parallel when the convective stability is varied

globally. Nonetheless, this suggests that the Hadley

cell is responsible for communicating the variations in

tropical convective stability to the storm tracks in the

midlatitudes. The role of the tropical convective stability

in eliciting a response in themidlatitude storm tracks has

not been previously identified. This result complements

the results found by Butler et al. (2010). It also raises

questions about the mechanisms facilitating the requi-

site tropical–extratropical interactions.

Using our simulations, we estimate the individual con-

tributions of changes in radiative equilibrium tem-

perature and tropospheric stability to the storm track

FIG. 3. Barotropic eddy kinetic energy as a function of latitude plotted across climates with increasingmean surface

temperature in radiative equilibrium. The convection scenario is stated above each plot. Here, ge is the convective

stability rescaling parameter within6108 of the equator; gx is the value outside of this latitude band. The white dotsshow the EKEmaxima, each marking the storm track location in the respective climate. The thick white dashed line

shows the terminus of theHadley cell, defined as the latitude at which the Eulerianmass streamfunction changes sign

at the altitude where it achieves its extremum.

FIG. 4. As in Fig. 3, but showing storm track response to convective stability variations.

9928 JOURNAL OF CL IMATE VOLUME 26

Cheikh Mbengue

Chia Chou

Katrina Hales

B. Langenbrunner

Kevin Quinn

Kathleen Schiro

Isaac Held’s Academic Family

Design: Momme Hell