impact of imposed drying on deep convection in a cloud ...sobel/papers/wang_sobel...impact of...

Impact of imposed drying on deep convection in a cloud-resolvingmodel

S. Wang1 and A. H. Sobel1,2,3

Received 7 September 2011; revised 5 November 2011; accepted 22 November 2011; published 28 January 2012.

[1] This study uses a cloud-resolving model under the weak temperature gradient (WTG)approximation to explore the response of deep convection to imposed drying. The drying,intended to mimic horizontal advection of dry air, is imposed as a linear relaxationof the humidity field toward zero within a specified layer. Radiative cooling and seasurface temperature are held constant and there is no mean vertical shear in the integrations.The statistically steady responses to drying in the lower, middle, and upper freetroposphere are compared. The rain rate decreases with drying when that drying is imposedin the lower or middle free troposphere, more strongly so for lower tropospheric drying.The decrease in rainfall is linearly proportional to the drying to a good approximation.Upper-tropospheric drying has almost no impact on the rain rate. For lower-troposphericdrying, the decrease in rain rate with drying can be well explained by assuming that both anappropriately defined normalized gross moist stability and surface turbulent fluxesremain constant as drying varies. For middle- and upper-tropospheric drying, thenormalized gross moist stability decreases with drying, allowing the precipitation todecrease less rapidly or not at all. The variations in normalized gross moist stability in turnresult from changes in the large-scale vertical motion profiles. These are top-heavy forweak or no drying, becoming somewhat less so as the strength of the drying increases.Over most of the range of drying strengths, the changes to the shape of the vertical motionprofile are greatest for upper tropospheric drying and smallest for lower troposphericdrying. For very strong lower tropospheric drying, however, the vertical motion profilebecomes bottom-heavy and the normalized gross moist stability becomes negative.

Citation: Wang, S., and A. H. Sobel (2012), Impact of imposed drying on deep convection in a cloud-resolving model,J. Geophys. Res., 117, D02112, doi:10.1029/2011JD016847.

1. Introduction

[2] Atmospheric moist convection plays critical roles inregulating tropical circulations on a wide spectrum of tem-poral and spatial scales, ranging from high-impact weather,to intraseasonal variability, to large-scale overturning circu-lations. Yet our understanding of tropical convection’sinteraction with larger scales is limited, particularly as thatunderstanding is expressed by convective parameterizationsin climate models. Incorrect sensitivity of parameterizedconvection to environmental humidity has become widelyrecognized as a critical factor limiting model performance[e.g., Derbyshire et al., 2004]. In nature, convection andhumidity interact in a complex fashion. The causal linkbetween humidity and convection is often difficult to dis-entangle. A more humid free troposphere may cause

stronger convection but may also be in part a consequenceof convective transport. In this study, we probe humidity-convection interaction by studying the impact of imposeddrying on statistically steady moist convection using a cloudresolving model.[3] Several studies have explored the impact of moisture

perturbations on convection, either using single columnmodels with parameterized convection [e.g., Derbyshireet al., 2004; Sobel and Bellon, 2009, hereafter SB09], orcloud-resolving models (CRMs) with explicitly resolvedconvection [e.g., Lucas et al., 2000; Takemi et al., 2004;Kuang, 2010; Tulich andMapes, 2010; James andMarkowski,2010]. Using the weak temperature gradient approximation,SB09 explored the impact of imposed drying in specifiedvertical layers on parameterized convection interacting withlarge-scale dynamics. They found that drying in the middlelayer was more effective than drying in the lower layer insuppressing deep convection, in both of two very differentsingle column models (SCMs). On the other hand, studiesusing cloud-resolving models by Tulich and Mapes [2010]and Kuang [2010] both showed that sensitivity to moistureperturbations in the lower troposphere was greater than tothose in the middle or upper troposphere. SB09 suggestedthat the weaker response to lower tropospheric drying in their

1Department of Applied Physics and Applied Mathematics, ColumbiaUniversity, New York, New York, USA.

2Department of Earth and Environmental Sciences, ColumbiaUniversity, New York, New York, USA.

3Lamont-Doherty Earth Observatory, Columbia University, New York,New York, USA.

Copyright 2012 by the American Geophysical Union.0148-0227/12/2011JD016847

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 117, D02112, doi:10.1029/2011JD016847, 2012

D02112 1 of 14

http://dx.doi.org/10.1029/2011JD016847

results might be due to inadequate sensitivity of parameter-ized convection to lower tropospheric moisture, and that itwould be highly desirable to conduct similar experimentswith a cloud-resolving model.[4] In this study, following SB09, we continue to explore

convective responses to external humidity forcing with acloud-resolving model under the weak temperature gradient(WTG) approximation. Under WTG, large-scale verticalmotion is parameterized, allowing interaction between con-vection and the large-scale divergent circulation withoutexplicit simulation of the latter using the equations of motionon a large domain. With this method, not only the amplitudebut also the vertical structure of the large-scale verticalmotion is determined internally as part of the solution.Several studies using WTG have found that the parameter-ized vertical motion is top-heavy in deep convective condi-tions [e.g., Sobel and Bretherton, 2000; Raymond and Zeng,2005; Kuang, 2011; Wang and Sobel, 2011], although thedegree of top-heaviness may be sensitive to the details ofeither the implementation of WTG or the model physics.The top-heaviness in these SCM and limited area CRMstudies also agrees with previous studies of large-scale mockWalker circulations where top-heavy vertical motions occursover the local SST maximum in two-dimensional cloud-resolving simulations [e.g., Grabowski et al., 2000, Yanoet al., 2002]. A notable exception is the study by Raymondand Sessions [2007]. They performed WTG CRM simula-tions in which warming in the upper free troposphere andcooling below were added to a reference temperature profilederived from a radiative-convective equilibrium simulation,and found that the increased gravitational stability led tobottom-heavy mass flux profiles.[5] In nature, both bottom- and top-heavy vertical motion

profiles have been observed. In the tropics, because WTGbalance holds approximately, the vertical motion profiletends to be similar to the diabatic heating profile, which haslong been known to have its maximum at different levels indifferent geographic regions [e.g., Webster and Lukas,1992]. Back and Bretherton [2006] demonstrated that, inboth reanalysis data and climate models, top-heavy profilesare common in the west Pacific warm pool region, whilebottom-heavy profiles are more typical in the east PacificITCZ region. Yuan and Hartmann [2008] further demon-strated that, over a large range of time scales from severalhours to months, the “top-heaviness” of vertical motions isconsistent with the penetration depth of cloud systems.[6] The degree of bottom- or top-heaviness of the large-

scale vertical motion profile is important to the moist staticenergy (or moist entropy) budget, as it strongly influencesthe vertical advection of moist static energy and the asso-ciated gross moist stability [Neelin, 1997; Back andBretherton, 2006; Sobel, 2007; Frierson, 2007; Friersonet al., 2011]. The most important dynamical factors lead-ing to the occurrence of bottom-heavy vertical motion pro-files are unclear at present. One may interpret bottom-heavyascent as the ascending branch of a shallow meridionaloverturning circulation [Zhang et al., 2008; Nolan et al.,2007, 2010]. In the east Pacific, one argument [Sobel,2007] is that bottom-heaviness results from a local SSTmaximum with large gradients around it, leading to largesurface convergence by the Lindzen-Nigam mechanism[Lindzen and Nigam, 1987]; yet this local SST maximum is

not as warm as the warmest tropical oceans globally or evenregionally, resulting in only modest instability of the localprofile to deep convection. An additional factor, suggestedby both theoretical and observational studies [Sobel andNeelin, 2006, Peters et al., 2008] is that transient eddies(with time scales of days) may transport dry air into ITCZregions, limiting the penetration depth of convectionthrough entrainment processes. The importance of dry airintrusions has also been recognized in several case studies[e.g., Brown and Zhang, 1997; Redelsperger et al., 2002;Roca et al., 2005; Zuidema et al., 2006; Allen et al., 2009].On the other hand, the hypothesis that drying may inducebottom-heavy profiles was not supported by the results ofSB09 using parameterized convection. Here, we furtherexplore this drying hypothesis using CRM, and demonstratethat drying can indeed suppress deep convection and lead tobottom heavy vertical motion.[7] In section 2, we present our numerical experiment

design. This closely follows SB09, apart from differencesresulting from the inherent differences between SCMs andCRMs. A cloud-resolving model, documented in detail inthe work of Wang and Sobel [2011], is used to study con-vective response to the imposed drying. Results are pre-sented in section 3. Section 4 contains discussion andconclusions.

2. Numerical Model and Experiment Design

2.1. Numerical Model

[8] We use the Advanced Research Weather Research andForecasting (WRF) Model version 3.0 [Skamarock et al.,2008]. We have configured WRF to run under either theWTG or radiative-convective equilibrium (RCE) mode. Useof WTG allows two-way interaction between the explicitlysimulated convection and a parameterized large-scale verti-cal motion field. Details of our implementation of WTGhave been documented in the work of Wang and Sobel[2011]; the primary difference from that used in SCMstudies such as SB09 (but similar to other CRM studies, e.g.,Raymond and Zeng [2005], Raymond and Sessions [2007],Sessions et al. [2010]) is that the horizontal mean tempera-ture field in the free troposphere is not strictly held to aprescribed profile, but relaxed toward it on a specified timescale, here taken to be three hours. We adopt the followingphysics schemes: boundary layer turbulence and verticalsubgrid eddies are parameterized using the Yonsei University(YSU) scheme; horizontal subgrid eddies are treated usingSmagorinsky first-order closure; surface moisture and heatfluxes are parameterized following the Monin-Obukhovsimilarity theory; the Purdue-Lin scheme is used for cloudmicrophysics, and simplified radiative cooling (constant1.5 K/d cooling in the troposphere) is applied in place ofinteractive radiation. The horizontal and vertical advectionschemes are fifth-order and third-order accurate, respec-tively. Moisture and other scalars are advected using apositive definite scheme [Skamarock et al., 2008]. We usethe implicit scheme [Klemp et al., 2008] to damp unphysicalreflection of vertically propagating gravity waves in the top5 km of the numerical grid. These schemes (except theconstant radiative cooling) are commonly used for numeri-cal weather prediction.

WANG AND SOBEL: IMPACT OF DRYING ON DEEP CONVECTION D02112D02112

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[9] All the numerical experiments were performed withhorizontal grid spacing of 2 km and constant Coriolisparameter f = 0. We use 50 vertical levels with 10 levels inthe lowest 1 km and grid spacing gradually increasing to1.5 km near the model top �22 km. The computationaldomain has 96x96 horizontal grid points and doubly peri-odic lateral boundary conditions.

2.2. Numerical Experiments

[10] To facilitate the comparison between convection inour cloud resolving model and parameterized convection inthe single column models in SB09, we closely follow theirstrategy to design the numerical experiments.[11] We first use the RCE solution, computed over an SST

of 28 °C, to derive the target temperature profile for theWTG integrations. The WTG integrations are then carriedout over an SST of 30 °C, 2 °C higher than that over whichthe RCE was obtained. Without any imposed drying, theWTG equilibrium is quite rainy because the relatively highSST leads to high local instability. The solution in this caseis identical to the three-dimensional WTG experiment withSST = 30 °C in the work of Wang and Sobel [2011]. Therain rate in this case is �22 mm/d, much higher than theRCE rain rate at SST = 28 °C (�4.5 mm/d). This case ischosen as the control to allow us to explore a large range inthe strength of the imposed drying, since the imposed dryingtends to reduce precipitation. The WTG vertical velocity inthis control case is top-heavy, with a maximum value of �11 cm/s in the upper troposphere. Wang and Sobel [2011]showed that this top-heavy profile is remarkably self-simi-lar as SST varies above the RCE value (28 °C), retaining analmost identical shape and varying only in amplitude. Boththe top-heavy WTG vertical velocity and cloud mass fluxindicate the dominance of deep convection at SST = 30 °C.Here, with SST held constant at 30 °C, we carry out a set ofintegrations in which we impose drying with varyingstrength to isolate the impact of drying on the equilibratedsolution.[12] Drying is imposed as a relaxation of the domain

averaged water vapor mixing ratio to zero in the tendencyequation of moisture:

∂Qv∂t

þ ⋯ ¼ � Qv½ �tq

for h1 < h < h2; ð1Þ

where Qv is the mixing ratio of water vapor, tq is the timescale for the imposed drying, [ ] denotes the domain average,and h is the dry mass above the given level divided by totaldry mass and varies between 0 and 1. The relaxation isapplied only where the dry mass h (the WRF vertical coor-dinate) falls between h1 and h2. As in SB09, we imposedrying in three different vertical layers in three sets ofsimulations. We refer to these as the lower, middle, and

upper troposphere, corresponding to three ranges in h: (0.6,0.825), (0.375, 0.6) and (0.150, 0.375), respectively. Thesethree layers are nearly identical to the three pressure ranges:600–825 hPa, 375–600 hPa, 150–375 hPa in SB09.[13] The drying time scale, tq, is the control parameter that

is varied in each of the three sets of experiments, as shown inTable 1. It is useful to express the results not only in terms oftq, but also in terms of the vertically integrated energyremoval due to the drying, Fq:

Fq ¼ 1tq

Z h2h1

LQvmdhg

; ð2Þ

where g (9.81 m/2) is gravity, m is the dry mass in thecolumn, and L (2.5 � 106 J kg�1) is the latent heat ofvaporization.[14] The drying time scale cannot approach zero for

numerical reasons, as discussed in SB09. In this model,further drying (smaller tq) than the minimum values for tqshown here would produce negative moisture. As largeamplitude forcing (e.g., comparable to or greater than thesum of surface fluxes and radiative cooling) is used in manyof the integrations, we are not necessarily in the regime ofsmall amplitude perturbations as in the work of Tulich andMapes [2010] and Kuang [2010]. As will be shown below,however, linearity can hold remarkably well even for largedrying.[15] All the numerical experiments are integrated for

25 days. The last 15 days are averaged to obtain the statis-tically steady state, unless otherwise mentioned.

3. Results

3.1. Precipitation as a Function of Imposed Drying

[16] Figure 1 shows daily mean precipitation (P in mm/d)versus drying time scale tq (Figure 1a) and energy export Fq(Figure 1b). P decreases with respect to either increasedenergy export or decreased drying time scale. For lowerlayer drying, P is reduced from �22 mm/d with zero dryingto �4 mm/d with tq = 70 h (lowest value of tq). With amodest time scale (tq > 10 days) P remains high for themiddle layer drying case. With a further decrease in tq to30 h or an increase in Fq to 110 W/m

2, drying in the middlelayer is able to reduce rainfall to 15 mm/d. On the otherhand, drying in the upper layer has little impact on precipi-tation. P remains above 20 mm/d in this case even whenenergy export exceeds 50 W/m2; for the same amount ofenergy export, precipitation is substantially reduced in theother cases. This suggests that moisture at upper levels ismainly a result of convection rather than having a strongcausal influence on convection, as suggested by observa-tional studies [Sherwood, 1999; Sherwood and Wahrlich,1999; Straub and Kiladis 2002, 2003; Sobel et al., 2004].

Table 1. Time Scales of Imposed Drying for Three Sets of Experimentsa

Vertical Layer of Drying Drying Time Scales tq(days)

Lower layer drying 0.6 < h < 0.825 2.9167, 2.9375, 2.9583, 2.9792, 3.0, 3.0833, 3.1667, 3.25, 3.5, 3.75, 4, 4.5, 5, 5.625,6.25, 7.5, 8.75, 10, 12.5, 15, 20, 25, 37.5, 50, 75, 100 days

Middle layer drying 0.375 < h < 0.6 1.25, 1.375, 1.5, 1.67, 1.83, 2, 2.5, 3, 3.5, 3.92, 4, 5, 6, 10, 20, 25, 37.5, 50 daysUpper layer drying 0.15 < h < 0.375 0.25, 0.375, 0.5, 0.625, 0.75, 1, 1.5, 2, 3, 4, 6, 10, 20 days

aThe h values 0.15, 0.375, 0.6 and 0.825 correspond approximately to pressure levels 150, 375, 600, and 825 hPa, respectively.


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However, an interesting aspect is that precipitation is slightlyincreased by�1 mm/d in the upper layer drying experimentswith tq less than 1 day (Fq > 20 W/ m

2). Limited examina-tion by subsampling the latter time period of the integrations(when the rain rate is quasi-steady) suggest that this is not aresult of sampling error, although longer integrations wouldbe needed to be certain of this. It has been proposed, forexample, that drying can promote convection, becauseoverlaying of dry layers upon moist layers creates potentialinstability [Allen et al., 2009]; more analysis would beneeded to determine if our results support this idea.[17] The P versus Fq relationship is remarkably linear. Let

P = P0 � a Fq, where a is an empirical linear slope and P0 is

the value of P in the control case Fq = 0. If P and Fq are bothexpressed in energy units (W/m2), so that the slope a isnondimensional, the value of a is 3.1, 1.9, and �0.4 forlower, middle and upper layer drying, respectively. Thevalue of a = 3.1 for lower layer drying is nearly equal to theinverse of the normalized gross moist stability in thosesimulations, as discussed in section 3.5.[18] At a given drying time scale or energy export, lower

layer drying most efficiently suppresses convection com-pared with middle or upper layer drying. This result is con-sistent with other modeling studies [Tulich and Mapes,2010; Kuang, 2010]. Presumably because moisture atupper levels responds more or less passively to convectionand large-scale ascent, drying at upper levels has littleimpact.[19] Figure 1b also shows surface fluxes (the sum of latent

heat E and sensible flux H), versus Fq for all experiments. Incontrast to precipitation, surface fluxes vary little with Fq.For example, P decreases to the RCE value (4.8 mm/d) forlarge values of lower layer drying, but surface fluxes onlydecrease by less than 2 mm/d over this range, and remainmuch greater than the RCE value. It should be kept in mindthat these simulations do not include either ocean couplingor cloud-radiative feedback. These effects could qualita-tively change the relationship of the total turbulent surfaceflux E + H to precipitation, though without necessarilychanging the sum of that and vertically integrated radiativecooling, which is the total forcing of the moist static energybudget by diabatic processes.[20] In addition, Figure 1b shows the sum of surface

fluxes and vertically integrated radiative cooling (E + H +〈QR〉, where 〈QR〉 denotes vertical integrated radiativecooling QR); this is the total diabatic forcing of verticallyintegrated moist static energy, excluding the imposed dryingFq. This quantity becomes equal to and then slightly lessthan Fq only at the very largest values of the latter imposedin the lower layer. Thus the total diabatic forcing of verti-cally integrated moist static energy (including Fq) is positivefor all but those experiments with the strongest drying.[21] It is of interest to compare our Figure 1 to Figure 3 in

SB09, to note similarities and differences between theresponse to drying in our CRM and that in the SCMs used bythose authors. First, the P � Fq relationship was found bySB09 to be more or less linear in the GEOS SCM as Fq wasvaried from 0 to 80 W/m2. In the MIT SCM, the effect ofdrying was significant for Fq less than 20 W/m

2, and leveledoff at large drying in several cases. In our model, thereduction of precipitation occurs for Fq from 0 to greater150 W/ m2 and shows a remarkably linear relationship withFq for lower and middle layer drying. Second, in both theSCMs in SB09, injection of dry air in the middle tropospherewas more effective at suppressing precipitation, opposite tothe present study. Finally, injection of dry air in the uppertroposphere has different impacts in the two SCMs in SB09:the GEOS SCM shows little sensitivity, while in the MITSCM drying in the upper troposphere was most effective atsuppressing precipitation. Thus our model is more in linewith the GEOS model than with the MIT model in thisrespect as well as the linearity of the P � Fq relationship, butis inconsistent with both on the relative importance of lowerversus middle tropospheric drying.

Figure 1. (a) Precipitation versus drying time scale tq.(b) Various budget terms as a function of energy removalFq: precipitation, surface fluxes E + H, and sum of surfacefluxes and column-integrated radiation cooling E +H + 〈QR〉.The gray dashed line shows the quantity: P0 � Fq/MN0. Seediscussion in section 3.5.


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[22] Figure 2 shows energy removal due to imposed dry-ing, Fq, versus drying time scale tq. Consistent with SB09,the two quantities are compactly related, with a nearly con-stant slope in the log-log plot for all the three cases.

3.2. Large-Scale Vertical Velocity

[23] Figure 3 shows the large-scale WTG vertical motionversus energy export Fq. For small Fq, Wwtg is top-heavy inall experiments, peaking near 250 hPa. As Fq increases, thepeak value decreases and the profile appears to become lesstop-heavy. When Fq reaches approximately 150 W/m

2 forlower layer drying, Wwtg rapidly becomes bottom-heavywith a peak at �875 hPa and weak or even descendingvertical motion in most of the free troposphere. This bottom-heaviness does not occur even at the maximum values ofupper or middle tropospheric drying (though those are not aslarge as the maximum lower tropospheric drying), but thereduction of Wwtg is still clearly seen in the upper tropo-sphere. Convective mass fluxes (not shown) vary consis-tently with the variation in Wwtg, being reduced in the uppertroposphere as Wwtg becomes less top-heavy.[24] Figure 4 illustrates the time evolution of Wwtg versus

height in lower layer drying for two different drying timescales, tq = 3 and 10 days, associated with energy exportFq = 153 and 52 W/m

2. These two cases represent two dis-tinct regimes: 1) at tq = 3 d, intermittent ascent and descentare both seen at upper levels, while steady ascent is seen atlower levels. The time-averaged Wwtg is bottom heavy. 2) Attq = 10 d, there is only steady ascent; there is no peakdetectable at lower levels, indicating that the low level peakemerges because of imposed drying.[25] Variations of the WTG vertical motion may be further

quantified by examining its projection onto discrete verticalbasis functions [Fulton and Schubert, 1985]. Here wesimply chose the basis functions as sin (mp zH0), where H0 =14 km, and m is 1 or 2. This choice is different from that ofTulich et al. [2007], who performed vertical mode analysison resolved cloud-scale vertical motions. With our chosen

basis functions, projection of WTG vertical motion Wm forthe mth mode is computed as

Wm ¼Z H00

Wwtg sin mpz

H0

� �dz=H0: ð3Þ

[26] In our implementation of WTG, temperature pertur-bations are related to WTG vertical motions by relaxingtemperature perturbations to zero. The coupling betweentemperature anomalies and WTG vertical motion occurs onthe WTG time scale, which is the same for all modes. Underthe implementation of WTG used by Kuang [2008, 2011]and Blossey et al. [2009], the coupling varies with thewave speed of each mode. We may expect some differencein these two different approaches.[27] The imposed drying reduces the amplitude of both the

first and second modes. This is illustrated in Figure 5a,which shows W1 and �W2 versus Fq. With Fq less than50 W/m2, drying causes more reduction in W1 for lowerlayer drying than for upper layer drying, while middle layerdrying appears to fall in between, much like variations ofprecipitation in Figure 1. Drying also causes reduction of�W2 in all cases, but unlike for W1, lower layer drying doesnot cause more reduction than middle and upper layerdrying. For lower layer drying, both W1 and �W2 becomeclose to zero or even negative for Fq � 150 W/m2.[28] The degree of top-heaviness may be further quanti-

fied by the ratio�W2/ W1, similar to Kuang [2011]. Withoutdrying, the ratio is �0.9. Figure 5b shows that the ratioremains nearly constant with Fq less than 100 W/m

2 forlower layer drying, but decreases to �0.7 with Fq �50 W/m2 for upper layer drying. Thus drying in the upperlayer leads to the most reduction in top-heaviness for thesame net energy removal, although it has the least impact onrainfall. This is explained in terms of the moist static energybudget below, in section 3.5. For lower layer drying, theratio �W2/ W1 eventually shows a sharp decrease to valuesclose to zero, indicating bottom-heavy WTG verticalmotions. Note that the numerical estimate of the ratiobecomes problematic when W1 approaches zero, as happensfor the largest values of Fq applied in the lower layer.

3.3. Vertical Profiles of Thermodynamic Variables

[29] Figure 6 illustrates vertical profiles of anomaloustemperature, water vapor mixing ratio, and moist staticenergy, as compared to the reference experiment withoutdrying, for the three sets of experiments. (For easy com-parison, the dark curves in Figure 6 indicate convectiveresponses with similar Fq � 45 W/m2). In all three variables,as the drying strength increases, convective responsesincrease as well. Convective responses are not limited to thevertical layer in which forcing is imposed. Negative tem-perature anomalies are found within a deep layer above theimposed forcing, while positive temperature anomalies arefound below the forcing layer (Figures 6a, 6d, and 6g). Thenode of this dipole structure in the temperature anomalies islocated at �1 km for lower layer drying, �3 km for middlelayer drying, and �6 km for upper layer drying. Moistureshows the largest reduction in the layer of imposed drying,but there is also significant drying aloft in the lower layerdrying case (Figure 6b) and below in the upper layer drying

Figure 2. Export of moist static energy Fq versus dryingtime scale tq on a log-log scale.


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Figure 3. WTG vertical velocity (cm/s) for (a) lower layer drying, (b) middle layer drying, and (c) upperlayer drying.


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case (Figure 6h), and general moistening within the bound-ary layer. Variations of MSE result from combinations oftemperature and moisture variations. MSE decreases in thefree troposphere and increases within the boundary layerwith strengthened drying. Reduction in MSE in the freetroposphere is mostly due to moisture reduction; consistentwith this, the peak moisture reduction corresponds in thevertical to the peak of variations of MSE in all cases.[30] The nonlocal impact of the imposed drying on tem-

perature and moisture is in line with other CRM studies.Tulich and Mapes [2010] and Kuang [2010] showed thatpositive humidity perturbations in the free troposphere causewarming at and above the layer in question, and that con-vection tends to counteract the humidity anomalies by cool-ing and drying that layer and the subcloud layer. These twostudies also showed stronger sensitivities of deep convectionto lower free-tropospheric perturbations than to upper tro-pospheric ones. Tulich and Mapes [2010] suggested that the

strong sensitivity to lower tropospheric anomalies was aconsequence of the marginal buoyancy maintained in thedeep lower tropospheric layer extending from surface to4 km. Nevertheless, comparison between our results andthose of Tulich and Mapes [2010] and Kuang [2010] is notentirely straightforward, because those two studies focusedon the responses to temperature and moisture anomaliesimposed at a specific time with no forcing thereafter, whilewe are interested in the statistically steady response to sus-tained forcing.[31] The positive anomalies of MSE and temperature

within the boundary layer may indicate weakened down-drafts. Supporting evidence comes from the consideration ofthe energy budget of the boundary layer. The primary termsin the budget are surface fluxes and the energy fluxes asso-ciated with updrafts and downdrafts at the top of theboundary layer. Because surface fluxes decrease with dry-ing, the increase of MSE within boundary layer can only be

Figure 4. Time series of WTG vertical velocity for (a) tq = 3 days and (b) 10 days for drying at lowertroposphere. Fq in these two experiments is 153 W/m

2 and 52 W/m2. (c and d) Time-averaged values ofWTG vertical velocity for the two cases.


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attributed to less energy loss at the top of the boundary layer,which is likely due to weaker downdrafts.

3.4. Precipitation–Relative Humidity Relation

[32] Observational studies [e.g., Bretherton et al., 2004;Peters and Neelin, 2006; Neelin et al., 2008; Holloway andNeelin, 2009] have examined the statistical relationshipbetween precipitation and column-integrated relative humidity(CRH, the column-integrated water vapor divided by itssaturation value) at daily and monthly time scales. Impli-cations of these relationships have been examined in theo-retical and modeling studies [e.g., Raymond, 2000;Raymond and Zeng, 2005; Sobel and Bellon, 2009; Mulleret al., 2009]. Here we examine this relationship in ourexperiments during the transition period from RCE to thenew WTG equilibrium under both imposed drying and

high-SST forcings. We sample the first 10 days of allexperiments after the higher SST, WTG, and drying are allswitched on, corresponding to a transition period from RCEto the new equilibrium achieved under both higher SST anddrying.[33] Figure 7 illustrates daily precipitation versus CRH for

the three sets of experiments. In all experiments, CRHremains greater than 0.6 and below 0.8. Over this narrowrange, neither quantity varies much for upper layer drying.For lower layer drying, P varies over a large range from 5 to20 mm/d (Figure 1) while CRH varies from 0.6 to 0.8. Formiddle layer drying, the same P is associated with lowerCRH and the apparent slope of the P-CRH relationship isalso less, compared to lower layer drying. There is littleoverlap between the two sets of points. Apparently theP-CRH relationship is not universal even within this singlemodel, but depends to some extent on the particular large-scale forcings with which convection is interacting.[34] The GEOS SCM in SB09 (their Figure 8) seems to

have a similar P-CRH relationship to that in our study. Inparticular, the ranges of CRH (0.6–0.8) and P (5–25 mm/d)in this model are both very close to our results. However,these two variables in the MIT SCM in SB09 vary overdifferent ranges, with CRH in particular varying between0.4 and 0.6. In this respect as well, the GEOS SCM behavesmore similarly to our CRM results than does the MIT SCM.

3.5. Moist Static Energy Budget

[35] The gross moist stability is a critical parameter inthermodynamic theories relating precipitation to tropicallarge-scale circulations, but remains under constrained byeither observations or numerical modeling. It has often beenassumed to be a small positive constant [e.g., Neelin andHeld, 1987]. Recent observational studies [López Carrilloand Raymond, 2005, Figure 4; Back and Bretherton, 2006]and numerical simulations [e.g., Bretherton et al. 2005;Raymond and Fuchs, 2009; Raymond et al., 2009], on theother hand, have found that it can assume negative values.[36] The budgets of vertically integrated moist static

energy (h) and dry static energy (s) in the statically steadystate can be written as

Wwtg∂s∂z

� �¼ H þ P þ QRh i and Wwtg ∂h∂z

� �¼ E þ H þ QRh i � Fq;

ð4Þ

where P, H, E, and QR denote precipitation, surface sensibleflux, latent flux and radiative heating, respectively. 〈 〉 =

Rp0pT

rdz denotes the mass-weighted vertical integral from thebottom to the top of the computational domain, where r isdensity. Substituting and rearranging terms yields the fol-lowing diagnostic relation [Sobel, 2007],

P ¼ 1MN

E þ H þ QRh i � Fq� �� QRh i � H ; ð5Þ

where we have defined MN, the normalized gross moiststability:

MN ¼ Wwtg ∂h∂z� �

= Wwtg∂s∂z

� �: ð6Þ

Figure 5. (a) Projection of Wwtg to the first mode, W1(thick symbols) and the second mode, W2 (�W2, thinsymbols). (b) The ratio �W2/W1, indicating top-heaviness.


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[37] This is essentially identical to the “gross moiststability ratio” used in the work of Sobel and Bellon [2009],with the only difference that the latter was computed in pres-sure coordinates. We denote the nominator and denominatoras Ah and As, which represent the vertically integrated verticaladvection of moist and dry static energy, respectively, by theWTG vertical velocity. A relation similar to but slightly

different from (6) is obtained if moisture convergence isused instead of vertical advection of dry static energy as thenormalization factor in the definition of MN [e.g., Raymondet al., 2009]. To estimate MN, we sample the model dataevery 12 h, then compute the time and domain averages ofAh and As, separately, and finally divide them. Our simpleradiative scheme produces nearly constant vertically

Figure 6. (a, d, g) Drying induced anomalous temperature T (K), (b, e, h) water vapor mixing ratioQ (g/kg), and (c, f, i) MSE (J/kg) for lower (Figures 6a–6c), middle (Figures 6d–6f), and upper(Figures 6g–6i) drying. The legend of the colorbar denotes the corresponding energy export Fq. The darkcurves in each panel indicate the response for Fq � 45 W/m2. The gray dots in Figures 6b, 6e, and 6hindicate the vertical levels of the imposed drying.


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integrated radiative cooling of �145 W/m2 (it can vary by�1 W/m2). The surface fluxes increase slowly and roughlylinearly with drying Fq, as shown in Figure 1b.[38] Figure 8a showsMN versus the energy export Fq in all

the cases. MN remains positive for most experiments, exceptfor a few with large drying imposed in the lower layer. Theslope of the relationship between MN and Fq is different inthe three cases. For upper layer drying, MN decreases overthe small range (0.3–0.15) when Fq is less than 50 W/m2.For middle layer drying, MN remains constant for Fq <50 W/ m2, then gradually decreases for Fq > 80 W/ m

2, butremains positive (�0.15). For lower layer drying, MN isnearly invariant when Fq < 100 W/ m

2, and then turns neg-ative sharply at the largest values of Fq where the total moiststatic energy forcing (including Fq) becomes negative (seeFigure 1b and accompanying discussion in section 3.1).[39] The normalized gross moist stability MN can vary due

to either vertical advection of moist static energy, Ah, orvertical advection of dry static energy, As. We first considerAh. Equation (4) indicates that vertical advection of moiststatic energy need not be simply related to precipitation.However, equation (4) and Figure 1b together show that theenergy removal due to drying, Fq, is mostly balanced byvertical advection, because variations in surface fluxes(Figure 1b) and radiation are both very small compared tothose in Fq. Hence, Ah varies similarly with respect to Fq forall three cases, as illustrated in Figure 8b. However, As mustco-vary with precipitation, as can be deduced from the drystatic energy equation (4). Figure 8b also shows that As hasslopes very similar to those in the P � Fq relation inFigure 1b. Therefore, variations in MN are mainly relatedto As, but not to Ah, which varies similarly for drying indifferent layers.

[40] Variations of Ah and As can also be illustrated in thephase space in Figure 8c. MN corresponds to the ratio Ah/As.The ratio is relatively constant for large Ah or As. In thelower layer drying experiments, when Fq falls between 140and 160 W/m2, As is reduced to values close to zero andvariations in MN become large, while the total MSE forcingE + H + 〈QR〉 � Fq becomes small and then changes sign.[41] Figure 8 can be compared to Figure 10 of SB09. MN

estimated in SB09 varies over large ranges in the two SCMs.The overall reduction of MN in our model is broadly con-sistent with that in the GEOS model. That model also showsnegative MN in response to sufficiently strong drying in thelower layer; the negative values occurred for Fq greater thanabout 70 W/m2, about half that required to cause negativeMN in our results. On the other hand, MN in the MIT SCMincreases with respect to drying.[42] The accuracy of the computation of MN can be

quantified by comparing the estimated P using equation (5)against the directly simulated P. Figure 9 shows that thebudget-derived estimates of P (thick symbols) compare wellwith directly simulated values. The steadiness assumed byequation (5) is not strictly satisfied, but the small deviationsof estimated P from the directly simulated values suggestthat transients have only a minor effect in these integrations.[43] The constancy of MN for integrations with lower tro-

pospheric drying over most of the range of Fq suggests aparticularly simple interpretation of that case. The dashedgray line in Figure 1b shows the quantity P0 � Fq/MN0where P0 and MN0 are the values of P and MN when Fq = 0.From equation (5), this is the precipitation which wouldoccur if neither surface fluxes nor the normalized grossmoist stability MN varied from their values in the absence ofimposed drying (recall that radiative cooling is constrained

Figure 7. Precipitation (mm/d) versus column relative humidity (CRH) for the lower, middle and upperlayer drying.


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Figure 8. (a) Normalized gross moist stability for the lower, middle and upper layer drying. Several largevalues at Fq greater than 130 W/m

2 are shown in a separate scale. (b) Ah and As versus drying time scale tq.(c) Ah versus As.


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to be nearly constant). The precipitation variations wouldthen simply be equal to the imposed drying magnified by theinverse of the constant normalized gross moist stability.Since the latter and the unperturbed surface fluxes areknown from the solution with no drying, this could beviewed as a predictive perturbation theory for the responseof precipitation to drying, given the unperturbed solution.The figure shows that the resulting estimate is remarkablyaccurate. (In fact it is fairly accurate even for large Fq, whereMN is not at all constant; the agreement there is apparentlyaccidental.) For drying in the middle troposphere, MNdecreases with Fq while the quantity in parentheses in (5)—the primary variable part of the forcing—remains positive;decrease in that quantity due to increasing Fq is partiallycompensated by decreasing MN, leading to a muted responsein precipitation compared to the lower tropospheric dryingcase. For upper tropospheric drying, the compensation isalmost perfect so that P remains nearly constant.[44] These results illustrate some of the subtleties inherent

in constructing theories based on the vertically integratedmoist static energy budget. For our integrations with lowertropospheric drying, that budget appears to offer a usefulinterpretation. Because the normalized gross moist stabilitystays nearly constant, a simple perturbation theory canexplain the response to imposed drying given only theforcing Fq and information about the unperturbed case. Forupper tropospheric drying, the opposite is true. The result(constant precipitation) can be stated very simply. Yet itsexplanation in terms of the moist static energy budget ismore complex, involving cancellation of the imposed dryingby changes in the normalized gross moist stability, which inturn result from changes in vertical structure as shown inFigure 5. The case of middle tropospheric drying liesbetween these two extremes. It is not clear to us that one

could have anticipated this varied behavior beforeperforming and analyzing the model integrations.

4. Discussion and Conclusions

[45] We have explored the response of convection toimposed drying using a cloud-resolving model under theweak temperature gradient approximation. The drying isimposed in three layers—in the lower, middle and upper freetroposphere—in three sets of model integrations, to mimicadvection of dry air into rainy regions in these distinct layers.Design of our numerical experiments closely follows Sobeland Bellon [2009]. The main findings can be summarizedbelow.[46] Daily rain rates decrease with drying when the drying

is imposed in the lower or middle free troposphere. Thedecrease in precipitation is quite linear with respect to drying,even when the energy export by drying reaches 150 W/m2.Drying in the lower free troposphere is most effective insuppressing convection and reducing rainfall, while drying inthe upper troposphere has little impact, and drying at middlelayers falls in between. The linear slope of precipitationversus energy export associated with drying is 3.1, 1.9, and�0.4 for lower, middle and upper tropospheric drying,respectively. For lower tropospheric drying, this slope is veryclose to the inverse of the normalized gross moist stability,which remains approximately constant over much of therange in drying strength and thus can be computed from theunperturbed case with no drying.[47] The parameterized large-scale vertical motion is top-

heavy over a large range of drying, but its vertical structureresponds differently to drying at different levels. While theamplitude of large-scale vertical motion, like precipitation,responds most strongly to lower tropospheric drying andleast to upper tropospheric drying, the opposite is true of theshape of the large-scale vertical motion profile and normal-ized gross moist stability. The vertical motion profilebecomes less top-heavy as upper tropospheric dryingincreases; this decreases the normalized gross moist stabil-ity, allowing precipitation to stay nearly constant despite theimposed drying. For lower-tropospheric drying, the shape ofthe vertical motion profile and value of the normalized grossmoist stability remain roughly constant as drying increasesover most of its range, allowing a strong decrease in pre-cipitation. For the largest values of lower tropospheric dry-ing, however, the vertical motion profile becomes bottom-heavy and the normalized gross moist stability becomesnegative. A parsimonious explanation of all these resultswould appear to be a challenging target for simple theoriesbased on the vertically integrated moist static energy budget.

[48] Acknowledgments. This work was supported by NSF grantAGS-1008847. We thank NCAR’s computational and Information SystemsLaboratory, where initial tests of our model were performed. Commentsfrom Stefan Tulich and two anomalous reviewers are greatly appreciated.

ReferencesAllen, G., G. Vaughan, D. Brunner, P. T. May, W. Heyes, P. Minnis,and J. K. Ayers (2009), Modulation of tropical convection by breakingRossby waves, Q. J. R. Meteorol. Soc., 135, 125–137, doi:10.1002/qj.349.

Back, L. E., and C. S. Bretherton (2006), Geographic variability in theexport of moist static energy and vertical motion profiles in the tropicalPacific, Geophys. Res. Lett., 33, L17810, doi:10.1029/2006GL026672.

Figure 9. Precipitation derived from the MSE budgetequation (5) (thick symbols), and directly simulated precipi-tation (thin symbols).


12 of 14

Blossey, P. N., C. S. Bretherton, and M. C. Wyant (2009), Subtropical lowcloud response to a warmer climate in a superparameterized climatemodel. Part II: Column modeling with a cloud-resolving model, J. Adv.Model Earth Syst., 1, 1–14, doi:10.3894/JAMES.2009.1.8.

Bretherton, C. S., M. E. Peters, and L. E. Back (2004), Relationshipsbetween water vapor path and precipitation over the tropical cceans,J. Clim., 17, 1517–1528, doi:10.1175/1520-0442(2004)0172.0.CO;2.

Bretherton, C. S., P. N. Blossey, and M. Khairoutdinov (2005), An energy-balance analysis of deep convective self-aggregation above uniform SST,J. Atmos. Sci., 62, 4273–4292, doi:10.1175/JAS3614.1.

Brown, R. G., and C. Zhang (1997), Variability of midtropospheric mois-ture and its effect on cloud-top height distribution during TOGACOARE, J. Atmos. Sci., 54, 2760–2774, doi:10.1175/1520-0469(1997)0542.0.CO;2.

Derbyshire, S. H., I. Beau, P. Bechtold, J.-Y. Grandpeix, J.-M. Piriou,J.-L. Redelsperger, and P. M. Soares (2004), Sensitivity of moist convec-tion to environmental humidity, Q. J. R. Meteorol. Soc., 130, 3055–3079,doi:10.1256/qj.03.130.

Frierson, D. M. W. (2007), The dynamics of idealized convection schemesand their effect on the zonally averaged tropical circulation, J. Atmos.Sci., 64, 1959–1976, doi:10.1175/JAS3935.1.

Frierson, D. M. W., D. Kim, I.-S. Kang, M. Lee, and J.-I. Lin (2011),Structure of AGCM-simulated convectively coupled equatorial wavesand sensitivity to convective parameterization, J. Atmos. Sci., 68, 26–45,doi:10.1175/2010JAS3356.1.

Fulton, S. R., and W. H. Schubert (1985), Vertical normal transforms:Theory and application, Mon. Weather Rev., 113, 647–658, doi:10.1175/1520-0493(1985)1132.0.CO;2.

Grabowski, W. W., J. I. Yano, and M. W. Moncrieff (2000), Cloudresolving modeling of tropical circulations driven by large-scale SSTgradients, J. Atmos. Sci., 57, 2022–2040, doi:10.1175/1520-0469(2000)0572.0.CO;2.

Holloway, C. H., and J. D. Neelin (2009), Moisture vertical structure,column water vapor, and tropical deep convection, J. Atmos. Sci., 66,1665–1683, doi:10.1175/2008JAS2806.1.

James, R. P., and P. M. Markowski (2010), A numerical investigation ofthe effects of dry air aloft on deep convection, Mon. Weather Rev.,138, 140–161, doi:10.1175/2009MWR3018.1.

Klemp, J. B., J. Dudhia, and A. Hassiotis (2008), An upper gravitywave absorbing layer for NWP applications, Mon. Weather Rev.,136, 3987–4004, doi:10.1175/2008MWR2596.1.

Kuang, Z. (2008), Modeling the interaction between cumulus convectionand linear waves using a limited domain cloud system resolving model,J. Atmos. Sci., 65, 576–591, doi:10.1175/2007JAS2399.1.

Kuang, Z. (2010), Linear response functions of a cumulus ensemble to tem-perature and moisture perturbations and implication to the dynamics ofconvectively coupled waves, J. Atmos. Sci., 67, 941–962, doi:10.1175/2009JAS3260.1.

Kuang, Z. (2011), The wavelength dependence of the gross moist stabilityand the scale selection in the instability of column integrated moist staticenergy, J. Atmos. Sci., 68, 61–74, doi:10.1175/2010JAS3591.1.

Lindzen, R. S., and S. Nigam (1987), On the role of sea surface temperaturegradients in forcing low-level winds and convergence in the tropics,J. Atmos. Sci., 44, 2418–2436, doi:10.1175/1520-0469(1987)0442.0.CO;2.

López Carrillo, C., and D. J. Raymond (2005), Moisture tendency equationsin a tropical atmosphere, J. Atmos. Sci., 62, 1601–1613, doi:10.1175/JAS3424.1.

Lucas, C., E. J. Zipser, and B. S. Ferrier (2000), Sensitivity of tropical westPacific oceanic squall lines to tropospheric wind and moisture profiles,J. Atmos. Sci., 57, 2351–2373, doi:10.1175/1520-0469(2000)0572.0.CO;2.

Muller, C. J., L. E. Back, P. A. O’Gorman, and K. A. Emanuel (2009), Amodel for the relationship between tropical precipitation and column watervapor, Geophys. Res. Lett., 36, L16804, doi:10.1029/2009GL039667.

Neelin, J. D. (1997), Implications of convective quasi-equilibria for thelarge-scale flow, in The Physics and Parameterization of MoistAtmospheric Convection, edited by R. K. Smith, pp. 413–446, Elsevier,Amsterdam.

Neelin, J. D., and I. M. Held (1987), Modeling tropical convergence basedon the moist static energy budget, Mon. Weather Rev., 115, 3–12,doi:10.1175/1520-0493(1987)1152.0.CO;2.

Neelin, J. D., O. Peters, J. W.-B. Lin, K. Hales, and C. E. Holloway (2008),Rethinking convective quasi-equilibrium: Observational constraints forstochastic convective schemes in climate models, Philos. Trans. R.Soc., Ser. A, 366, 2579–2602, doi:10.1098/rsta.2008.0056.

Nolan, D. S., C. Zhang, and S. Chen (2007), Dynamics of the shallowmeridional circulation around intertropical convergence zones, J. Atmos.Sci., 64, 2262–2285, doi:10.1175/JAS3964.1.

Nolan, D. S., S. W. Powell, C. Zhang, and B. E. Mapes (2010), Idealizedsimulations of the intertropical convergence zone and its multilevel flows,J. Atmos. Sci., 67, 4028–4053, doi:10.1175/2010JAS3417.1.

Peters, M. E., Z. Kuang, and C. C. Walker (2008), Analysis of atmosphericenergy transport in ERA-40 and implications for simple models of themean tropical circulation, J. Clim., 21, 5229–5241, doi:10.1175/2008JCLI2073.1.

Peters, O., and J. D. Neelin (2006), Critical phenomena in atmospheric pre-cipitation, Nat. Phys., 2, 393–396, doi:10.1038/nphys314.

Raymond, D. J. (2000), Thermodynamic control of tropical rainfall, Q. J. R.Meteorol. Soc., 126, 889–898, doi:10.1256/smsqj.56405.

Raymond, D. J., and Z. Fuchs (2009), Moisture modes and theMadden-Julian oscillation, J. Clim., 22, 3031–3046, doi:10.1175/2008JCLI2739.1.

Raymond, D. J., and S. L. Sessions (2007), Evolution of convection duringtropical cyclogenesis, Geophys. Res. Lett., 34, L06811, doi:10.1029/2006GL028607.

Raymond, D. J., and X. Zeng (2005), Modelling tropical atmospheric con-vection in the context of the weak temperature gradient approximation,Q. J. R. Meteorol. Soc., 131, 1301–1320, doi:10.1256/qj.03.97.

Raymond, D. J., S. L. Sessions, A. H. Sobel, and Z. Fuchs (2009), Themechanics of gross moist stability, J. Adv. Model. Earth Syst., 1, 1–20,doi:10.3894/JAMES.2009.1.9.

Redelsperger, J. L., D. B. Parsons, and F. Guichard (2002), Recoveryprocesses and factors limiting cloud-top height following the arrivalof a dry intrusion observed during TOGA COARE, J. Atmos. Sci.,59, 2438–2457, doi:10.1175/1520-0469(2002)0592.0.CO;2.

Roca, R., J. P. Lafore, C. Piriou, and J. L. Redelsperger (2005), Extratropicaldry-air intrusions into the West African monsoon midtroposphere: Animportant factor for the convective activity over the Sahel, J. Atmos.Sci., 62, 390–407, doi:10.1175/JAS-3366.1.

Sessions, S., S. Sugaya, D. J. Raymond, and A. H. Sobel (2010), Multi-ple equilibria in a cloud-resolving model using the weak temperaturegradient approximation, J. Geophys. Res., 115, D12110, doi:10.1029/2009JD013376.

Sherwood, S. C. (1999), Convective precursors and predictability in thetropical western Pacific, Mon. Weather Rev., 127, 2977–2991,doi:10.1175/1520-0493(1999)1272.0.CO;2.

Sherwood, S. C., and R. Wahrlich (1999), Observed evolution of tropicaldeep convective events and their environment, Mon. Weather Rev., 127,1777–1795, doi:10.1175/1520-0493(1999)1272.0.CO;2.

Skamarock, W. C., J. B. Klemp, J. Dudhia, D. O. Gill, D. M. Barker,M. G. Duda, X. Huang, W. Wang, and J. G. Powers (2008), A descrip-tion of the advanced research WRF version 3, Tech. Rep NCAR/TN–475+STR, Natl. Cent. Atmos. Res., Boulder, Colo.

Sobel, A. H. (2007), Simple models of ensemble-averaged tropical precip-itation and surface wind, given the sea surface temperature, in The GlobalCirculation of the Atmosphere, edited by A. H. Sobel and T. Schneider,pp. 219–251, Princeton Univ. Press, Princeton, N. J.

Sobel, A. H., and G. Bellon (2009), The effect of imposed drying on param-eterized deep convection, J. Atmos. Sci., 66, 2085–2096, doi:10.1175/2008JAS2926.1.

Sobel, A. H., and C. S. Bretherton (2000), Modeling tropical precipitationin a single column, J. Clim., 13, 4378–4392, doi:10.1175/1520-0442(2000)0132.0.CO;2.

Sobel, A. H., and J. D. Neelin (2006), The boundary layer contribution tointertropical convergence zones in the quasi-equilibrium tropical circula-tion model framework, Theor. Comput. Fluid Dyn., 20, 323–350,doi:10.1007/s00162-006-0033-y.

Sobel, A. H., S. E. Yuter, C. S. Bretherton, and G. N. Kiladis (2004), Large-scale meteorology and deep convection during TRMM KWAJEX, Mon.Weather Rev., 132, 422–444, doi:10.1175/1520-0493(2004)1322.0.CO;2.

Straub, K. H., and G. N. Kiladis (2002), Observations of a convectivelycoupled Kelvin wave in the eastern Pacific ITCZ, J. Atmos. Sci., 59,30–53, doi:10.1175/1520-0469(2002)0592.0.CO;2.

Straub, K. H., and G. N. Kiladis (2003), The observed structure of con-vectively coupled Kelvin waves: Comparison with simple models ofcoupled wave instability, J. Atmos. Sci., 60, 1655–1668, doi:10.1175/1520-0469(2003)0602.0.CO;2.

Takemi, T., O. Hirayama, and C. Liu (2004), Factors responsible for thevertical development of tropical oceanic cumulus convection, Geophys.Res. Lett., 31, L11109, doi:10.1029/2004GL020225.


13 of 14

Tulich, S. N., and B. E. Mapes (2010), Transient environmental sensitivitiesof explicitly simulated tropical convection, J. Atmos. Sci., 67, 923–940,doi:10.1175/2009JAS3277.1.

Tulich, S. N., D. A. Randall, and B. E. Mapes (2007), Vertical-mode andcloud decomposition of large-scale convectively coupled gravity waves ina two-dimensional cloud-resolving model, J. Atmos. Sci., 64, 1210–1229,doi:10.1175/JAS3884.1.

Wang, S., and A. H. Sobel (2011), Response of convection to relative SST:Cloud-resolving simulations in two and three dimensions, J. Geophys.Res., 116, D11119, doi:10.1029/2010JD015347.

Webster, P. J., and R. Lukas (1992), TOGA COARE: The coupledocean–atmosphere response experiment, Bull. Am. Meteorol. Soc., 73,1377–1416, doi:10.1175/1520-0477(1992)0732.0.CO;2.

Yano, J.-I., W. W. Grabowski, and M. W. Moncrieff (2002), Mean-stateconvective circulations over large-scale tropical SST gradients, J. Atmos.

Sci., 59, 1578–1592, doi:10.1175/1520-0469(2002)0592.0.CO;2.

Yuan, J., and D. L. Hartmann (2008), Spatial and temporal dependence ofclouds and their radiative impacts on the large-scale vertical velocityprofile, J. Geophys. Res., 113, D19201, doi:10.1029/2007JD009722.

Zhang, C., D. S. Nolan, C. D. Thorncroft, and H. Nguyen (2008),Shallow meridional circulations in the tropical atmosphere, J. Clim., 21,3453–3470, doi:10.1175/2007JCLI1870.1.

Zuidema, P., B. Mapes, J. Lin, C. Fairall, and G. Wick (2006), The interac-tion of clouds and dry air in the eastern tropical Pacific, J. Clim., 19,4531–4544, doi:10.1175/JCLI3836.1.

A. H. Sobel and S. Wang, Department of Applied Physics and AppliedMathematics, Columbia University, New York, NY 10027, USA.([email protected])


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