modifications of the atmospheric moisture field as a...

Quarterly Journal of the Royal Meteorological Society Q. J. R. Meteorol. Soc. 142: 30–42, January 2016 A DOI:10.1002/qj.2625

Modifications of the atmospheric moisture field as a resultof cold-pool dynamics

Linda Schlemmera,b* and Cathy Hoheneggera

aMax Planck Institute for Meteorology, Hamburg, GermanybInstitute for Atmospheric and Climate Science, ETH Zurich, Switzerland

*Correspondence to: L. Schlemmer, Max Planck Institute for Meteorology, Bundesstrasse 53, 20146 Hamburg, Germany.E-mail: [email protected]

This study investigates the interplay between atmospheric moisture and deep convectiveclouds via cold-pool dynamics in the absence of large-scale forcing in a series of cloud-resolving modelling studies. More specifically, the contribution of moisture advection,evaporation of rain and surface fluxes to the moisture budget over particular regionsof the domain is investigated. This is done both for a continental case and an oceaniccase although both cases show very similar behaviour. The accumulation of moisture inconfined regions of the sub-cloud layer that constitute preferred locations for future clouddevelopment mainly results from the advection of moisture. The latter contributes ∼86%,minor evaporation of precipitation contributes ∼4%, whereas surface moisture fluxes yield∼11% in the continental case. In the oceanic case advection contributes ∼125%, surfacemoisture fluxes ∼ −32% and evaporation of precipitation ∼7%.

To further identify the origin of the advected moisture, additional scalars markingmoisture originating from the surface and from the evaporation of rain are introducedinto the model. It is seen that the surface moisture and the evaporated rain water releasedwithin the last 2 h only make 55% of the moisture accumulated in the moist patches in theland case, the rest stemming from older moisture. In the ocean case, this share increasesto 72%. The contribution of recently released moisture drops to 28% at cloud base in thecontinental case and to 56% in the ocean case. The contribution at cloud base is dominatedby surface fluxes; the evaporation of rain is negligible.

Key Words: clouds; convection; cold pools; moisture budget

Received 15 January 2015; Revised 24 June 2015; Accepted 1 July 2015; Published online in Wiley Online Library 23September 2015

1. Introduction

There is a two-way interaction between the atmospheric moisturedistribution and the development of convective clouds. On theone hand, convective clouds prefer moist environments for theirgrowth (e.g. Holloway and Neelin, 2009; Sherwood et al., 2010)and are hampered in dry surroundings (e.g. Redelsperger et al.,2002). On the other hand, convection itself constitutes oneof the atmospheric processes that can modify the moisturedistribution, in the free atmosphere mostly through verticaltransport of moisture and detrainment, and in the sub-cloudlayer through the evaporation of precipitation. Moreover, cloudshave the ability to change the moisture distribution by creatingsecondary circulations (e.g. Hartmann et al., 1984), throughdynamical modulation by cold-pool wakes (e.g. Seifert and Heus,2013; Schlemmer and Hohenegger, 2014; Li et al., 2014) orby modifying the surface moisture fluxes through their controlon surface radiation as well as on near-surface temperature andmoisture. As such, the question of the origin of moisture is centralto the question of the processes controlling the development of

convection. Focusing on the life cycle of deep convection asexperienced through its diurnal evolution, one aspect of thisdiscussion concerns the importance of moisture advection versuslocal moistening. The observational study of Kumar et al. (2013)has shown that, in the hours preceding the onset of heavyrainfall events, the relative humidity is increased in the middletroposphere and that it is rather large-scale dynamical, not small-scale, processes that dominate the evolution from shallow todeep convection. Pointing in a similar direction, Davies et al.(2013) found moisture convergence and vertical velocity stronglyrelated to strong convective precipitation. Masunaga (2013)went a further step and worked on identifying the causes forthe moistening of the free troposphere observed within a fewdays before peak convection in the Madden–Julian Oscillation(MJO). In a budget analysis he found convective eddies andlarge-scale moisture transport through cloud base to be equallystrong in the background state, whereas large-scale motions werecontrolling the cloud-base moisture flux prior to the occurrenceof highly organized systems. Focusing on the transition fromshallow to deep convection over a continental site, Zhang andKlein (2010) identified a higher mixing ratio between 2 and

c© 2015 Royal Meteorological Society

Moisture Modifications by Cold Pools 31

4 km on days where a transition to deep convection occurred.Moreover, horizontal convergence of water vapour and a strongerboundary-layer inhomogeneity were present on deep convectiondays. Estimating the time-scales needed for sufficient moisteningof the atmosphere for deep convection to occur, Hoheneggerand Stevens (2013) concluded that large-scale moisture advectiondominates the moistening process. Congestus moistening of thefree troposphere was too slow to explain the observed rapiddeepening of convective clouds. Hence advection dominates overdetrainment.

Even in the absence of large-scale forcing, the question of theorigin of moisture and of the importance of dynamical effectspersists. Does the moisture that feeds clouds simply originatefrom surface moisture fluxes or are other moistening processesimportant? The question is highly tied to the existence of coldpools. Cold pools, driven by the evaporation of precipitation andmelting of hydrometeors have been mentioned as an importantingredient for the organization of convective clouds into largerstructures (e.g. Byers and Braham, 1949; Kuang and Bretherton,2006; Tompkins, 2001) and for the transition from shallow todeep convection (e.g. Khairoutdinov and Randall, 2006).

Cold pools may affect the development of convection by locallyincreasing the sub-cloud moisture field and/or by dynamicallifting. In simulations of shallow cumulus convection during theRain in Cumulus over the Ocean (RICO) campaign, Seifert andHeus (2013) observed a tight coupling of the cloud field to thesub-cloud layer cold-pool-influenced moisture field promotingthe clustering process of clouds. Li et al. (2014) found generallymoister and warmer updraughts in regions that are influencedby cold-pool outflows in RICO simulations. In the study ofSchlemmer and Hohenegger (2014) on diurnal cycles of deepconvection, a size argument was put forward. Larger areas ofincreased moisture foster the formation of wider clouds, whichare less affected by lateral entrainment and become deeper.Moreover the moist-patch regions are the areas where dynamicallifting occurs in connection with the moistening. Feng et al. (2015)looked at the differences between isolated and intersecting coldpools during the transition from shallow to deep convectionin the AMIE/DYNAMO∗ field campaign. They identified acloser alignment of convective clouds in combination with amore frequent occurrence of stronger secondary updraughtsfor intersecting cold-pool boundaries as factors promoting theorganization of deep convection. The study of Tompkins (2001)argued that it is purely the thermodynamic modification of thesub-cloud layer that promotes new cloud formation where themoist areas are more buoyant than other areas.

Despite highlighting different mechanisms, the previouslymentioned studies all emphasized the formation of moist regionsin the sub-cloud layer as important for the future development ofconvection. Zhang and Klein (2010) observed that boundary-layervariations in temperature, wind speed, and mixing ratio signif-icantly increased after 1330 local time (LST) on deep convectiondays. Thereby, precipitation precedes the variability of tempera-ture and wind indicating that the temperature and wind variabilityare products of precipitation and possibly cold-pool dynamics. Incontrast to temperature and wind, they find moisture variabilityleading precipitation in late-afternoon precipitation events.

Both a moistening and a drying of the area directly linked to theimpinging of the downdraught are theoretically possible. On theone hand, the evaporation of rain yields a direct moistening. Onthe other hand, the transport of drier air from the free atmosphereinto the sub-cloud layer by the downdraughts results in a drying.The observational study of Barnes and Garstang (1982) identifieda threshold rain rate of 2 mm h−1 that separates these two cases.Tompkins (2001) highlights the evaporated rain as major sourceto this moistening, whereas the studies by Seifert and Heus (2013),Schlemmer and Hohenegger (2014) and Li et al. (2014) list as

∗ARM (Atmospheric Radiation Measurement) MJO Investigation Experiment/Dynamics of the MJO.

an additional contributor the environmental moisture that isadvected from outside the cold-pool regions by the cold-poolwake. A further source for the observed moistening could be anenhancement of the surface moisture fluxes. Increased moisturefluxes from the surface into the atmosphere under the influenceof cold pools have been documented in numerous observational(e.g. Young et al., 1995) and modelling (e.g. Ross et al., 2004)studies due to the increased wind speed and humidity differencebetween the atmosphere and the surface.

This study aims to investigate the mechanisms leading to anaccumulation of moisture in specific areas of the sub-cloud layerand to quantify the individual contributions to the moisture field.The focus is on how cold-pool dynamics influence and modulatethe sub-cloud layer moisture field under the absence of large-scaleforcing. The mechanisms under scrutiny are advection of pre-existing moisture by cold pools, locally confined enhancement ofmoisture by rain evaporation, moistening of the sub-cloud layerby surface latent heat fluxes (which may vary spatially), and acombination of these effects. The contribution of the individualterms of the moisture budget will be quantified and the historyof moisture will be tracked. This will be investigated in a case ofa diurnal cycle of continental convection which is characterizedby a rather deep and dry sub-cloud layer. The surface latent heatflux arises from evapotranspiration. In addition, a case will beexamined of maritime convection with a shallow and moist sub-cloud layer where surface latent heat flux arises from evaporationfrom the sea surface. Generally, cold pools are more vigorous overland. The study of Engerer et al. (2008) documented changes intemperature as strong as −12 K for continental organized systems,whereas the DYNAMO field campaign over the Indian Ocean andthe Tropical Ocean–Global Atmosphere (TOGA) field campaignover the Equatorial Western Pacific reported temperature changesfor cold pools of up to −3 K (Young et al., 1995; Feng et al., 2015).

The question of the origin and the creation or conversionprocesses for different masses of air are crucial in many areas ofresearch. Different approaches have been taken in studies on thecoupling between the land surface, the sub-cloud layer, cloudsand the free atmosphere. While a number of studies includedmassless Lagrangian particles in their numerical codes to trackback the history of air masses (e.g. Heus et al., 2008; Yeo andRomps, 2012), further studies have made use of a more indirectway to identify the sources by including tracers emitted duringspecific processes. Risi et al. (2008) studied the modification andresulting distribution of stable water isotopes in deep convectiveclouds, whereas Devine et al. (2006) marked air originatingfrom the ocean surface by dimethyl sulphide (DMS) to studythe influence of cold pools on sea–air fluxes. Couvreux et al.(2010) expanded the idea of using naturally occurring tracersand introduced concentration tracers into the model to label airarriving from the surface with the goal of isolating the portionof surface air in convective updraughts. We develop this ideaeven further and introduce two additional scalars that are emittedwhenever surface latent heat fluxes are active or evaporation ofrain occurs, respectively. As in Devine et al. (2006) and Couvreuxet al. (2010), the additional tracers will be subject to a decaywith a given time-scale, related to the time-scale of the process inquestion and thus will only exist for a limited amount of time.

The set-up of the model and the experiment is explained insection 2, the simulations are presented in section 3 followed byan analysis of the moisture budget in section 4, and the evolutionof additional passive tracer fields in section 5. A summary is givenin section 6.

2. Method

2.1. Model

Simulations are performed using the University of California,Los Angeles (UCLA) Large-Eddy Simulation (LES) model (seeStevens et al., 2005) in a set-up similar to Schlemmer and

c© 2015 Royal Meteorological Society Q. J. R. Meteorol. Soc. 142: 30–42 (2016)

32 L. Schlemmer and C. Hohenegger

Hohenegger (2014). The UCLA-LES solves the three-dimensionalOgura–Phillips anelastic equations, where one assumes anisentropic background state. The prognostic variables are thethree components of the wind velocity (u, v, and w), the totalwater mixing ratio qt, the liquid water potential temperature θl

and the microphysical species. The UCLA-LES uses a third-orderRunge–Kutta scheme for the time integration, a fourth-ordercentred scheme for the advection of momentum and a flux-limitedfourth-order upwind scheme for the advection of scalars. ASmagorinsky-type scheme is employed to represent subgrid-scale(sgs) mixing. A two-moment ice microphysics scheme includingice, snow, graupel and hail as cold species developed by Seifertand Beheng (2006) is used. Over land, sgs surface fluxes of heatand moisture are calculated using a simple land-surface model(Rieck et al., 2014). The surface resistance is calculated followingthe Jarvis–Stewart parametrization (Jarvis, 1976) and depends onthe leaf area index (LAI), the incoming short-wave radiation, thesoil moisture content, the vapour pressure deficit and the surfacetemperature. A four-layer soil scheme is employed to calculatesoil temperature and moisture. The soil temperature is calculatedby solving the heat diffusion equation, whereas the vertical fluxof water is determined by conduction and diffusion. As a lower-boundary condition, the soil model has a prescribed climatologicalmean temperature and moisture. Rain infiltration at the upperboundary is not considered. Over ocean, fluxes are calculatedemploying similarity theory given a fixed sea-surface temperature.Radiative fluxes are calculated using the ‘correlated-k’ method,whereas radiative transfer is approximated utilizing a δ-four-stream method (Fu and Liou, 1993; Pincus and Stevens, 2009).

2.2. Identification of cold pools and moist patches

As the study focuses on the moisture modulation by cold pools,an objective identification of both cold pools and moist areasis needed. We follow the method proposed in Schlemmer andHohenegger (2014) and define cold pools via the departure �θe inequivalent potential temperature from its horizontal mean value.As soon as �θe falls below a threshold of −2 K, a pixel is identifiedas a cold pool. Connected pixels are then clustered. To identify fea-tures that exhibit a certain vertical extent, we apply the procedureto θe, which is the equivalent potential temperature θe which hasbeen density-weighted vertically averaged over the lowest 500 m.Likewise the moist areas are identified by calculating the pertur-bation �qt of the 0–500 m density-weighted vertically averagedtotal water mixing ratio with respect to its horizontal mean value.Regions which exceed a threshold of 0.8 g kg−1 are identifiedand clustered. These connected moist regions are termed ‘moistpatches’. As the upper limit of 500 m lies below the cloud base inall the simulations, qt is equal to the water vapour mixing ratio qv.As in Schlemmer and Hohenegger (2014), the chosen thresholdsinfluence the area of the identified objects but do not affect theconclusions of this study. Performing the identification of coldpools and moist patches and the analysis on two-dimensionalfields instead of three-dimensional fields allows for a high sam-pling rate in time. The analysis is performed every 60 s.

The main motivation to use θe to identify cold pools lies inits conservation property under condensation and evaporation,and in the fact that it records both the temperature and moisturesignal. The temperature depression in the cold pool can therebybe linked to the shape of the θe profile in the vertical and the heightof origin of the downdraught (cf. Schlemmer and Hohenegger,2014). The moist patches with their high values of θe are bydefinition not part of the cold pool itself, even though the wakeregion of the cold-pool gravity current with increased moisturebelongs to the moist patch.

2.3. Additional scalars

In order to trace specific contributions to the moisture field,additional scalars are introduced into the model. These scalars

track specific source and sink terms of qt, namely evaporation ofrain and sgs surface moisture fluxes, and are advected and diffusedwith the same numerical routines as qt. The sublimation of anycold species is assumed to be of minor importance and thus isnot considered. Note that the melting of cold hydrometeors is animportant contribution to the formation of cold pools in termsof temperature. However for the qt budget the cold species mustenter the rain class before converting to water vapour. Moistureoriginating from the evaporation of rain is tracked by the tracerdenotedM, whereas moisture resulting from sgs surface moisturefluxes is tracked by the tracer S . The conservation equations forthe two tracers read:

∂M∂t

= −v · ∇M + ∂

∂tM

∣∣∣∣diff

+ ∂

∂tM

∣∣∣∣micro

− Mτ

, (1)

and∂S∂t

= −v · ∇S + ∂

∂tS

∣∣∣∣diff

+ ∂

∂tS

∣∣∣∣sfc

−Sτ

, (2)

where v is the three-dimensional wind vector. The first termon the right-hand side represents advection, the second onethe turbulent sgs diffusion and the third evaporation of rain orconvergence of sgs surface fluxes, respectively.

The tracers undergo a decay process with a time-scale τ , whichis covered by the fourth term on the right-hand side of Eqs (1)and (2):

∂C

∂t= −C

τ, (3)

where C represents the scalar. A value of τ = 7200 s is chosen inorder to capture the travel of the scalar into the moist patch andsome persistence there. A value of 3600–7200 s corresponds tothe typical lifetime of observed cold pools (cf. Feng et al., 2015).Typical wind speeds in the divergent wind field of the cold poolare ∼5 m s−1 and a typical cold-pool radius is 10 km. It thus takes2000 s for a tracer to travel from the interior to the edge of thecold pool. Assuming a sub-cloud layer depth of 1 km and a speedof 1 m s−1 for the up- and downdraughts, 2000 s must be addedin order to capture the tracer on its way from the cloud baseto the surface in the cold pool, and up to cloud base again inthe moist-patch region. Thus, the value of 7200 s is chosen. Inorder to estimate the sensitivity of the results to the value of τ ,two additional experiments using τ = 3600 s and a case withoutdecay (τ → ∞) are conducted.

The only sink term considered is the decay process. This meansthat, as soon as a portion of the moisture gets the label S orM, it keeps that label independently of further transformationprocesses. It is especially not removed through autoconversion oraccretion. This choice is first a matter of definition and relates tothe period over which one wants to track the moisture. Second,the analysis focusses on the lowest 500 m, which is below cloudbase. A potential inconsistency which could nevertheless arise isthat some portion of M or S reaches altitudes where accretionor autoconversion should have taken place before re-enteringthe lowest 500 m. However, we assume that the ascribed decayprocess has already set in by then.

The emission of the tracers begins at model start. In the casewithout decay, a restart of the simulation using τ = 7200 s isperformed at 1200 LST and the decay terms neglected thereafter.Analogous to qt, the density-weighted vertically averaged 0–500 mfields of M and S are M and S , respectively.

The tracers are reminiscent of the study of Couvreux et al.(2010), who used concentration tracers to label air arriving fromthe surface. The current study represents the traced quantities bytheir value at the time of release; this is a different choice fromthe study of Couvreux et al. (2010) who emitted a tracer with aconstant concentration of 1 at the surface. One should keep inmind that the employed scalars give an integrated informationabout the processes that have affected the air mass. However



(a) (b)

Figure 1. Initial profiles of (a) θe (K) and (b) relative humidity (%) for the LAND,WET and OCEAN cases.

they are unable to convey exact information about the time andplace of the emitting process. If the concentration is higher,more of the scalar has been emitted and/or the emission hastaken place more recently. If the concentration is lower, fewerscalars have been released and/or the release was longer ago.However there is no unique solution to finding the emissionrate, time and place given the current concentration of the scalar.This means that M will be high in places where evaporation ofrain has taken place, which is primarily the centre of the coldpool. Without wind, M would simply decay over time at thatlocation and be diffused out by turbulent transport. Howeverin the divergent wind field of the cold pool, the scalar will betransported away like qt and may end up accumulated in themoist patch, as advocated in Tompkins (2001). On the otherhand, S will be distributed over the entire domain with anincrease of the concentration close to the surface. Larger valueswill be found in places where latent heat flux is increased. Thelonger the air mass in question has not had contact with thesurface, the smaller the concentrations of S will become. At agiven time the sum of M and S is not expected to equate to qt.The remaining moisture is ‘old’ moisture which has experiencedneither evaporation nor sgs surface moisture fluxes recently.Thus, a share of qt is possibly covered multiple times, once by qt,and additionally by S or M. One could introduce further scalarswhich represent ‘old’ moisture. This would cause an additionalburden in computational memory and power without deliveringnovel information.

In a first step, we tried to use Lagrangian particles insteadof the passive tracers to track the emitting process. It turnedout to be very difficult to draw any robust conclusion from theresults as the flow field in the vicinity of downdraughts andcold-pool wakes is highly turbulent, the Lagrangian particlesare advected with a different advection scheme than qt, andthe budget along trajectories was hard to close. Moreover, theparticles are transported with w inside the downdraught, whereasthe hydrometeors fall with the sedimentation velocity, leadingto inconsistencies. The passive scalars now employed offer atreatment consistent with qt which is essential to derive an exactbudget. If the Lagrangian particles were given a label wheneverthey are exposed to evaporation of rain or sgs surface moistening,with the label decaying over time, then the particles would carrya recent label in those places where M or S are high.

2.4. Set-up

The main investigated case corresponds to an idealized diurnalcycle of convection over midlatitude continental areas, closelyfollowing the simulations of Schlemmer and Hohenegger (2014).In contrast to Schlemmer and Hohenegger (2014), the sgs surface

fluxes are calculated interactively. The initial atmospheric profileis characterized by a constant lapse rate of temperature of−7 K km−1 starting from a surface temperature of 18 ◦C , anda zonal, easterly wind that increases from 2 m s−1 at the surfaceto 17 m s−1 at the jet-stream height and decreases to westerlywinds in the stratosphere. The humidity of the atmosphere liesbetween the values of the WET and DRY simulation of Schlemmerand Hohenegger (2014) with a relative humidity of 75% closeto the surface decreasing to 45% in the middle troposphere.The vertical distribution of θe and the relative humidity of thesimulations is displayed in Figure 1. Settings for the land surfacemodel are identical to Rieck et al. (2014) with the saturation ofthe soil set to 58% close to the surface increasing to 71% at adepth of 1.39 m, an LAI of 2.96 and a vegetation cover of 100%.The temperature of the uppermost soil layer is set to 291.14 Kand decreases to 289.92 K at 1.39 m depth. The latitude of thesimulation domain is set to 48.0◦N. This run is termed ‘LAND’in the following.

As the contribution of M to qt depends on evaporation andhence on the rain rate, a second simulation is performed whichproduces a higher rain rate. This simulation is identical to LANDbut features a relative humidity of 85% close to the surfacedecreasing to 55% in the middle troposphere (identical to theWET simulation of Schlemmer and Hohenegger, 2014). It istermed ‘WET’ in the following.

To test further the generality of the results, a maritime casewithout wind is simulated. The initial conditions stem froma sounding taken from the German research vessel Polarsternat 08◦N, 11.658◦W at 1200 UTC on 1 May (Hohenegger andStevens, 2013). The SST is set to a constant value of 302.5 K inthe simulation. In contrast to Hohenegger and Stevens (2013),the interactive radiation scheme is switched on. The latitude ofthe simulation domain is set to 0◦N. This simulation is termed‘OCEAN’.

The computational domain comprises 1024 × 1024 × 120grid points for all simulations, corresponding to 256 × 256 km2

in the horizontal. The horizontal grid spacing is 250 m. In thevertical a stretched grid with a spacing of 20 m up to 1000 mand vertical stretching beyond is used. The first full modellevel is situated at 10 m. The top of the model is at 19 773 mwith a sponge layer starting at 14 939 m. Doubly periodic lateralboundary conditions are used and the Coriolis force is neglected.In the initialization phase, white random noise with an amplitudeof 0.2 K (0.05 g kg−1) is applied to the temperature (moisture)field in the lowest 200 m. Simulations are integrated startingfrom 0500 LST, in LAND and WET until 1800 LST, and inOCEAN until 0700 LST on the following day. The differentintegration times are chosen as the transition to deep convectionproceeds more slowly in OCEAN, whereas in LAND and WET thephenomena of interest are restricted to the time when significantsurface buoyancy fluxes are present. The 2D fields θe, qt, Mand S are written to disk every 60 s. In OCEAN, output of2D fields starts at 1800 LST, when sufficient organization ofthe sub-cloud layer has developed. 3D fields are written every30 min.

3. Simulation overview

Figure 2 documents the evolution of the liquid and frozenhydrometeors as well as the surface buoyancy fluxes andprecipitation rate. In LAND, first shallow clouds develop from0830 LST onward and deepen until the early afternoon. Iceprocesses have already set in by 0930 LST. Clouds deepenprogressively until they reach their maximum depth around1730 LST at a height of 12 km. The surface precipitation followsthe cloud development with an onset at 1000 LST and maximumvalues between 1400 and 1600 LST. Maximum values at specificpoints of the domain reach ∼50 mm h−1 at 1700 LST. Sgs surfacefluxes of heat and moisture show a pronounced diurnal cyclewith a peak around 1200 LST (Figure 2(d)). The midday Bowen



heig

ht

(m)

time (LST)

(a) (b) (c) (d)

time (LST) time (LST)

W m

–2

g kg–1

rain

rate

(m

m h

–1)

time (LST)

Figure 2. Time–height plots of domain-mean values of the sum of cloud liquid and rain mixing ratio (shading, g kg−1), the sum of cloud ice, snow, graupel and hailmixing ratios (contours, g kg−1, with the same contour intervals as the shaded areas, and the 10−4 g kg−1 contour dashed) and surface rain rate (black dashed line,W m−2) for (a) LAND, (b) WET and (c) OCEAN. Panel (d) shows domain-mean values of simulated sensible (grey) and latent (black) heat fluxes (W m−2) for LAND(solid), WET (long dashes) and OCEAN (short dashes).

timeocean (LST)

timeland (LST)

–15 –100–20

–100 –50 50 100

–1.2e-03

–8.0e-04

–4.0e-04

4.0e-04

8.0e-04

1.2e-03

0.0e+00

0

–50–12

–9

–6

–3

ma

x �� e

in c

old

pool (K

)

eva

pora

tion r

ate

(m

m h

–1)

(a)

(b) (c)

Figure 3. (a) Diurnal cycle of �θe in cold pools. The dashed lines indicate the domain-mean evaporation rate (mm h−1) integrated over the lowest 500 m. Tocompute �θe, the largest temperature perturbation found within all cold pools is picked at each time step. (b) �qt distribution (shading, kg kg−1), identified coldpools (black contours), moist patches (dark blue areas) and active clouds (red contours) in LAND at 1700 LST. (c) Distribution of the different terms of the qt budgetin LAND at 1700 LST for the subdomain indicated by the solid black square in (b). Blue contours indicate the micro term (contour of 2.2×10−7 kg kg−1 s−1), orangecontours the sgs term (value of −2.2×10−7 kg kg−1 s−1) and the red contours (value of 2.2×10−7 kg kg−1 s−1). The adv term is indicated by the dark green (value of−5×10−6 kg kg−1 s−1) and the light green (value of 5×10−6 kg kg−1 s−1) contours. Black contours indicate the boundaries of the cold pools and grey areas the moistpatches.

ratio amounts to roughly 0.5. In WET, clouds deepen morequickly and hold higher concentrations of both warm and coldhydrometeors. As a consequence, surface rain sets in earlier(starting from 0900 LST) and values are increased. The dailyprecipitation sum in WET is 4.0 mm versus 2.5 mm in LAND.In OCEAN, the cloud base lies lower and clouds deepen moreslowly. The phase of shallow convection lasts until 2200 LSTafter which cold microphysical processes set in. Clouds reacha maximum height of 13 km at 0600 LST on the second day.Domain-mean surface precipitation is reduced compared toLAND, and maximum rain occurs in the early morning. Howevermaximum rain rates at single grid points are larger in OCEANthan in LAND and values of up to 80 mm h−1 are reached, albeitbriefly. Over the last 24 h of the simulation, a precipitation sum of0.81 mm is recorded. The surface heat fluxes show little variationover time. As expected, latent heat fluxes are with a value of100–120 W m−2 higher than sensible heat fluxes, which remainsmaller than 20 W m−2.

As soon as precipitation sets in, distinct cold pools start toform (Figure 3). Some very small and shallow cold pools arealready detected by the algorithm before the onset of first rainat the surface. They may either be signatures of rain which hasevaporated entirely before reaching the surface, or products ofturbulence. The cold pools are visible as near-surface regions ofdecreased θe. The maximum decrease of �θe reaches values of−8.7 K in LAND at 1750 LST, −9.1 K at 1404 LST in WET, and−14.7 K at 0640 LST on the second day in OCEAN. The timeevolution of the domain mean �θe closely follows the surfacerain rate (compare Figures 3(a) and 2). The �θe depressionis mostly determined by the θe difference between the middletroposphere and the surface as downdraughts transport low-θe

air into the sub-cloud layer. This difference is larger in WET thanin LAND and even larger in OCEAN, where a moist sub-cloudlayer is combined with a relatively dry free troposphere (Figure 1).However the radial extent of the cold pools is larger in LANDthan in OCEAN. This is related to higher evaporation rates inLAND (dashed line in Figure 3(a)) resulting in more negativelybuoyant air, more intense cold pools and greater propagationspeeds. The evolution of the θe difference in LAND and WETfollows the progress of the rain and evaporation rate, yieldingan earlier signal in �θe in WET and comparable values in theevening. Cold pools cover at most 10% of the domain in LANDand at most 5% in OCEAN.

In combination with the cold-pool formation and as describedin Schlemmer and Hohenegger (2014), the sub-cloud layermoisture field is modified. Dry regions inside the cold poolsthat are encircled by moister regions are observed (Figure 3(b)).The maximum �qt amounts to 2.1 g kg−1 at 1532 LST in LAND,2.4 g kg−1 at 1440 LST in WET, and 1.5 g kg−1 at 0615 LST on thesecond day in OCEAN. Moist patches cover at most 5% of thedomain in LAND and at most 2% in OCEAN. The cloud fieldbegins to organize strongly in LAND and OCEAN with the onsetof rain, whereby convective clouds form preferentially in thoseareas where the moisture is increased and vertical lifting is present.These areas are the wake zone of the cold pools and the areaswhere opposing cold pools may collide. The formation of cloudswith a larger diameter is fostered, which promotes a reductionof lateral entrainment and enables a deepening of the clouds.This can be partly recognized by the fact that the deepening ofthe clouds lags the precipitation evolution in Figure 2. For moredetail about the underlying processes, refer to Schlemmer andHohenegger (2014).



4. Moisture budget

In order to identify the mechanisms leading to the redistributionof moisture in the sub-cloud layer and especially to the formationof moist patches as seen in Figure 3, the budget of qt is analysed.The budget of qt reads:

∂

∂tqt =−v · ∇qt + ∂

∂tqt

∣∣∣∣micro

+ ∂

∂tqt

∣∣∣∣diff

+ ∂

∂tqt

∣∣∣∣sfc

=−v · ∇qt + ∂

∂tqt

∣∣∣∣micro

+ ∂

∂tqt

∣∣∣∣sgs

=−vh ·∇hqt−w· ∂

∂zqt+ ∂

∂tqt

∣∣∣∣micro

+ ∂

∂tqt

∣∣∣∣sgsh

+ ∂

∂tqt

∣∣∣∣sgsv

.

(4)

The first term on the right-hand side on the first line representsadvection, the second one microphysical conversion processes,the third the sgs diffusion, and the fourth the convergence ofsgs surface moisture fluxes. The diff and sfc terms are takentogether as an sgs term, which represents turbulent diffusion dueto unresolved eddies or thermals. Further, the advection termand the sgs term are split into their horizontal (−vh · ∇hqt andsgs h) and vertical (−w · ∂qt/∂z and sgs v) parts. The individualterms are extracted during the model run from the respectiveroutines. In the diffusion routine of the model, the sfc fluxes aregiven as the lower-boundary condition. Above the surface, thediff term acts. Thus, the complete sgs is extracted but one shouldkeep in mind that two different processes are represented: the sgssurface moisture flux convergence directly at the surface and theturbulent diffusion in the atmosphere. We have checked that theextracted budget closes exactly, i.e. the change of qt at each gridpoint equals the extracted ∂qt/∂t term, which in turn is equal tothe sum of the individual components.

For the analysis of the qt budget, all the contributing termshave been density-weighted vertically averaged (Eq. (5)) with theintegration bounds z0 = 0 m and z1 = 500 m, and the air densityof the background state in the anelastic system ρ0. Transport ofqt across the upper lid bounding qt is captured by the adv v andsgs v term.

∂

∂tqt =

−z1∫

z0

ρ0 vh ·∇hqt dz −z1∫

z0

ρ0w· ∂

∂zqt dz +

z1∫z0

ρ0∂

∂tqt

∣∣∣∣micro

dz +z1∫

z0

ρ0∂∂t qt

∣∣∣∣sgsh

dz +z1∫

z0

ρ0∂∂t qt

∣∣∣∣sgsv

dz

z1∫z0

ρ0 dz

= advh +advv +micro+ sgsh + sgsv = adv + micro + sgs. (5)

Figure 3(c) illustrates the spatial distribution of the differentterms. The micro term shows a positive contribution where theevaporation of rain consumes latent heat. Evaporation is activein young cold pools (e.g. label B in Figure 3(c)), whereas in theolder, larger ones evaporation is no longer active (e.g. label A inFigure 3 (c)). The adv term shows mostly positive values, whichare aligned with the wake region of the gravity current. The sgsterm is almost exclusively positive, active over the entire domainand expresses the turbulent mixing that arises in the daytimeconvective boundary layer. Larger values of adv and sgs seem tobetter align with the location of the moist patches than the microterm.

Figure 4 shows area averages of the individual terms of thebudget. In Figure 4(d) the adv term shown in (a–c) is split upinto its horizontal (adv h) and vertical (adv v) part. The sumover all components for the domain mean in LAND (Figure 4(a))is slightly positive until clouds set in. The clouds then lead toa transport of qt out of the sub-cloud layer until ∼1230 LST.This is visible in the negative contribution from adv v, yieldingan overall negative tendency. After 1230 LST the sub-cloud layer

is in an approximate moisture balance between sgs moisteningand advection. Convergence of vertical sgs fluxes moisten thesub-cloud layer, whereas the convergence of horizontal sgs fluxesis zero when averaged over the entire domain. There is a positivecontribution from the evaporation of precipitation after 1100 LST,which leads to an overall moistening given that sgs and adv canceleach other.

The budget is conditionally averaged over the cold-pool andmoist-patch regions every 60 s to get an idea about the processesacting in these specific locations. The advection terms can beunderstood recalling the flow pattern of a cold pool. Thedowndraught penetrates into the sub-cloud layer and createsby reason of continuity a divergent near-surface wind field.The conditional averaging employed in the qt budget analysiscorresponds to a volume integral which is bounded by thebottom surface, the upper lid at 500 m, and the cold-pool andmoist-patch boundaries along the sides. The volume integral canbe converted into a surface integral using Gauss’s theorem. Thus,only the fluxes through the upper lid and the surface boundingthe cold pools and moist patches in the horizontal contribute tothe adv term. Inside the cold-pool areas (Figure 4(b)) there is astrong drying primarily caused by horizontal advective transportof qt out of the cold pools. This adv h term can be explainedby continuity arguments, as it nearly compensates the adv vby the downdraught. Important to note is that the residual isnegative and constitutes the dominant term of the budget. Inthe moist-patch regions (Figure 4(c)) the advection of moistureremains the main contributor to the qt budget although thepicture is reversed: advection of moisture into these areas yieldsa positive tendency. The strong horizontal advection is to a largedegree balanced by vertical advection. Hence, in the moist-patchregion there is pronounced moisture-flux convergence, which iscompensated by vertical fluxes out of the sub-cloud layer. Theevaporation of precipitation is stronger in the cold pools than inthe moist patches, as expected from Figure 3(c), but overall playsa minor role. While the moistening by sgs fluxes is positive incold-pool areas, it is first negative inside the moist patches andturns positive after 1230 LST, when sgs h overcompensates sgs v.The horizontal sgs flux convergence is negative inside the moist

patches. This stems from the down-gradient turbulent transportof increased moisture values there. Averaged between 1430 and1800 LST, the time of deep convection, advection contributes85.6%, sgs moistening 10.7% and evaporation 3.7% to the totalqt tendency in the moist-patch regions.

The terms of the budget are averaged in time over the timespan of deep convection to assess the generality of the resultsfound in LAND. The time span of deep convection is defined tostart when the domain-mean value of the sum of all warm andcold hydrometeors first exceeds a threshold of 10−4 g kg−1 at aheight of 10,100 m (cf. dashed contour in Figure 2). With thisdefinition, deep convection starts at 1200 LST in WET, 1430 LSTin LAND and 0000 LST in OCEAN. Results are displayed togetherin Figure 4(e–g) to assess the generality of the result. In WETthe picture looks very much comparable to LAND. The higherrain rates yield a slightly enhanced contribution to the microterm averaged over the domain. However, in cold pools, theevaporation is slightly reduced. This is presumably caused by adrier sub-cloud layer in LAND which favours evaporation of rain.



(a) (b) (c) (d)

(e) (f) (g) (h)

Time [LST] Time [LST] Time [LST] Time [LST]

Figure 4. Different terms of the qt budget for (a) domain mean, (b) cold-pool areas and (c) moist-patch areas in LAND. In (a) the solid grey lines illustrate the meancloud-base and cloud-top heights and the grey dashed line the domain-mean rate rate. In (d) the advection term shown in (a–c) is split up into its horizontal (longdashed) and vertical (short dashed) parts. Note that the magnitude for the moist patches in (d) has been scaled by a factor of 0.1. Panels (e–g) show different terms ofthe qt budget averaged between 1430 and 1800 LST in LAND, 1200 and 1800 LST in WET, and 0000 and 0700 LST in OCEAN for (e) the domain mean, (f) cold-poolareas and (g) moist-patch areas. Panel (h) shows adv (circles), adv h (squares) and adv v (diamond) terms averaged over the same times.

Above all, evaporation still provides the smallest contributor.Advection terms are slightly enhanced in cold pools and slightlyreduced in moist patches, but remain the dominant term.Averaged between 1200 and 1800 LST, advection contributes77.3%, sgs fluxes 17.4% and evaporation 5.4% to the total qt

tendency in the moist-patch regions. Even though precipitationis enhanced in the WET simulation, evaporation still plays aminor role.

In OCEAN the picture also looks comparable to LAND.There is an export of moisture out of the sub-cloud layer byvertical advection (adv v<0) which is compensated by sgs v,such that the total tendency becomes close to zero, indicativeof a sub-cloud layer in equilibrium (Figure 4(e)). The adv termprimarily determines the evolution of moisture inside the coldpools (Figure 4(f)) and moist patches (Figure 4(g)) through itshorizontal component, whereas the evaporation of precipitationconstitutes the smallest contribution to qt. Inside cold pools,the relative contribution from the micro term is neverthelessenhanced in OCEAN compared with LAND. The overall sgscontribution is positive in the cold pools and negative in themoist patches, due to a larger negative sgs h than positive sgs vpart. Averaged between 0000 and 0700 LST, advection contributes125.0%, sgs fluxes −32.1% and evaporation 7.1% to the total qt

tendency in the moist-patch regions. Thus, the cold pools drywith time due to the advection term, whereas the latter termmoistens the moist patches and moistening by evaporation playsa minor role, validated for LAND, WET and OCEAN. It shouldbe noted that the conditionally sampled area changes over timeas cold-pool and moist-patch boundaries evolve. The qt budgetrestricted to those areas is thus not closed. In fact, the qt content ofthe specific areas stays more or less constant with time (consistentwith their definition). The tendencies shown in Figure 4 are ratherreflected in a deformation of the boundaries as pixels cross thethreshold used. Since we are interested in the processes that drivethe local changes in the moisture distribution, this is not an issuehowever.

Figure 4 indicates that the moistening by the sgs v term, whichis dominated by the moistening resulting from convergence of sgssurface fluxes, is not enhanced in the moist-patch region, whichmight appear counter-intuitive. To understand the differentbehaviour of the sgs v term in different areas of the domain,the individual controls on the sgs v term are analysed. The

sgs surface moisture fluxes are influenced by the wind speed,the near-surface saturation deficit, the surface roughness lengthand the atmospheric stability. Moreover, over land areas, thetranspiration by plants is modulated by the available surface netradiation, the soil moisture content and the surface temperature.In LAND and inside cold pools, wind speed is increased comparedwith the domain-mean value. However the stability is increaseddue to the cold air mass, which also reduces the saturationvapour pressure and thereby the saturation deficit. In the moist-patch regions, the wind speed is even more enhanced than inthe cold-pool areas, the saturation deficit is reduced and thestability is close to neutral. The incoming radiation is stronglymodulated by clouds. It is reduced in the centre of the cold pools,where the cloud of the parent convective cell causes shading, aswell as on the moist patches due to the development of newconvective cells. The combination of these various effects leadsin LAND (and WET) to sgs surface moisture fluxes of aboutequal magnitude in moist-patch and cold-pool regions. Thesaturation deficit is enhanced in cold-pool regions in OCEAN,whereas it is reduced in moist-patch regions compared withthe domain-mean value given the respective temperature ofthe cold-pool and moist-patch regions. In OCEAN the moistpatches are rather cool regions, whereas they hold a temperaturebetween the domain-mean value and the cold-pool value inLAND. This means that the drying outweighs the cooling effectinside the cold pools and an additional cooling decreases thesaturation deficit in the moist-patch regions. This leads to anenhancement of the sgs moisture fluxes from the surface into theatmosphere inside the cold pools, and a decrease in the moist-patch areas.

Taking a closer look at vertical profiles of qt, sgs v, and theadv term in Figure 5 helps us to understand the processes actingbetween the surface and the cloud base. qt is first of all enhancedthroughout the whole sub-cloud layer in moist patches, whereasit is reduced inside the cold pools. Vertical diffusion transportsmoisture upwards and is mostly active in the lowest 200 m.Advection shows a slightly different picture in the sense that thedrying in the cold pools occurs close to the surface, whereas themoistening in the moist-patch occurs at a rather higher level (witha peak at 450 m). In OCEAN the advective moistening of moist-patch areas starts above ∼150 m. The vertical profiles of Figure 5in combination with the budget analysis of Figure 4 suggest that



heig

ht (m

)

(a) (b) (c) (d)

(e) (f) (g) (h)

heig

ht (m

)

qt (kg kg–1) sgs (kg kg–1 s–1) adv (kg kg–1 s–1) adv (kg kg–1 s–1)

qt (kg kg–1) sgs (kg kg–1 s–1) adv (kg kg–1 s–1) adv (kg kg–1 s–1)

Figure 5. Vertical profiles of (a, e) qt, (b, f) the sgs v term, (c, g) the adv term and (d, h) adv h and adv v terms horizontally averaged (avg), averaged over cold-poolareas (cp) and averaged over moist-patch areas (mp) for (a–d) LAND and (e–h) OCEAN simulations at 1702 LST (0502 LST on the second day) in LAND (OCEAN).

(a) (b)

Figure 6. Subsection of (a) distribution of qt (shading, kg kg−1), S (contours of 8×10−4 kg kg−1 (red) and 1×10−3 kg kg−1 (orange)),M (contours of 4×10−4 kg kg−1

(blue) and 6×10−4 kg kg−1 (grey)) and cloud-base convective mass flux (black, contour of 1 kg m−2 s−1). (b) Distribution of qt (shading, kg kg−1), S (red lines,contours of 4×10−4 kg kg−1 (thin solid), 8×10−4 kg kg−1 (thick solid) and 1×10−3 kg kg−1 (dashed)), M (blue lines, contours of 1×10−4 kg kg−1 (thin solid),4×10−4 kg kg−1 (thick solid) and 6×10−4 kg kg−1 (dashed)) at cloud-base height and cloud-base convective mass flux (black, contour of 1 kg m−2 s−1) in LAND at1700 LST. The subdomain and labels A and B are identical to Figure 3(c).

qt is transported outwards inside the cold pools in a shallow layerclose to the surface. Some upward turbulent transport occursduring the outward transport. In the moist-patch areas, wherevertical lifting is active (Figure 5(d)), this moisture is then liftedupward.

The moisture budget analysis has revealed that the moistpatches are primarily moistened by advection of moisture. Ashas been recognized in Figure 3(c), advection is enhanced ina thin region around the cold pool, the cold-pool wake. Henceadvection is primarily the result from the impinging downdraughtand resulting cold-pool dynamics.

5. Moisture tracking

Although having identified the advection term as the majorcontributor to the moisture budget of moist patches, the originalrelease mechanism for the moisture remains unclear. To thisend further scalars are included into the model which trackspecific origins of qt, namely qt originating from evaporation(M) and sgs surface moisture fluxes (S) (section 2.3). Thesescalars carry the information if a given air portion has beenexperiencing moistening by rain evaporation or sgs surface fluxes,

and indicate how much moistening has occurred through theseprocesses. Remaining moisture is ‘old’ moisture, meaning that ithas not been emitted by rain evaporation or sgs surface fluxesrecently. Concerning the decay time, which can be thought ofas a measure for the memory given to the process, a decay timeof τ = 7200 s is chosen (section 2.3). To test the sensitivity ofthe results to the decay time, two additional simulations usingτ = 3600 s and without decay (τ → ∞) for the LAND case areperformed. First, the spatial distribution of the tracers is exploredto understand their redistribution by cold-pool dynamics. Second,the contribution of the tracers to the evolution of qt is investigated.This is done both in the lowest 500 m where cold pools and moistpatches develop, and at cloud base height, where the formationof new, active convective clouds takes place. Active clouds aredefined as those clouds, where w >1 m s−1 and the cloud liquidwater mixing ratio exceeds 1.0×10−6 kg kg−1.

5.1. Spatial distribution of tracers

Figure 6 gives a visualization of the cloud field and the distributionof qt, M and S in LAND using τ7200 at 1700 LST for thesame subdomain shown in Figure 3(c). The cloud field shows a



strong organization in elongated patterns. Cold pools are visiblein the qt distribution as dry areas, which are surrounded byconfined regions of increased qt, the aforementioned moistpatches. Comparing Figure 6 with Figure 3(c), it becomes obviousthat the concentration of the tracers is not necessarily increasedat the same place where the emitting process is active, indicatingtransport. M is high in places where rain and direct evaporationoccurs (e.g. at labels A and B). M tends to be high in regionswhere qt is low. In addition, a radial spreading of M close to thesurface within the cold pools is discernible. At cloud-base height,narrow confined regions of increased values of M are visiblein areas where active clouds are found, although the overlap isnot as good as with S . These areas are the wakes of the coldpools, which transport the evaporated water out of the cold-poolcentres. It could also be evaporated rain from new convectivecells forming. In contrast, S tends to be low within the cold-poolareas where it is pushed outwards by the divergent flow field.S increases in narrow bands around the cold pools, where sgsis high and where lifting occurs (the moist-patch regions). Atcloud-base height, S is increased in regions where active cloudsare found. Hence comparison of the S and M distributionalready suggests a closer link between S and clouds than betweenM and clouds. The S distribution matches with the result ofDevine et al. (2006). They found spatial inhomogeneities in DMSgenerated by cold pools to be aligned with updraught regions. Itshould be noted that the distribution of S and M is not onlyinfluenced by cold-pool dynamics but also by sub-cloud-layereddies. In the cold-pool-free regions, where a regular convectiveboundary layer prevails, S shows strong variations with slenderregions with increased values, where the sub-cloud-layer eddiesshow upward movement. Small spots of increasedS at cloud baseare visible, presumably the tops of sub-cloud-layer eddies. Thisis in line with the sgs term shown in Figure 3(c) which showsturbulent moistening in the cold-pool-free sub-cloud layer.

To get a more quantitative idea about the spatial spreading ofqt, M and S from a source region, the decorrelation length D isdetermined. This is done by calculating the autocorrelation c ofqt at lag n at each point in time for each vector in the x direction:

c(n) =

Nx∑x=1

{qt(x) − ¯qt

} · {qt(x + n) − ¯qt

}σ 2

, (6)

where Nx is the number of points in the x direction, ¯qt the averagevalue of qt over this vector and σ the standard deviation of qt.Then, D is defined to be the average lag n at which c drops below0.5. The results from all vectors in the x direction are averagedacross y. D is computed equivalently in the y direction. The sameprocedure is applied to M and S . Because of the periodicity ofthe domain, the lag n can be chosen up to a value of Nx or Ny,respectively.

Figure 7 shows the decorrelation length for the different tracers.First, it is smaller in the x direction than in the y direction inLAND. Thus, the background wind leads to a dilution of thetracers in the zonal direction. In OCEAN the signal is symmetricin x and y, in accordance with the flow orientation. Second,decorrelation length-scales are larger in WET than in LAND.Further, decorrelation length-scales are larger in LAND than inOCEAN. The absence of wind and wind shear in OCEAN likelyexplains the smaller decorrelation length-scale in OCEAN thanLAND. In addition, and as mentioned in section 3, the spatialextent of the cold pools is larger in LAND. This can be explained bya drier sub-cloud layer, stronger evaporation of rain and increasedevaporative cooling, leading to a faster propagation speed (notshown). Thus the tracers are distributed over a larger area in thesub-cloud layer in LAND. This effect is even enhanced in WET,where more moisture is available. The time to travel from cloudbase to the surface and then from the centre of the cold pool tothe edges is ∼3000 s in LAND (with a typical cloud-base height

(m)

Timeland (LST)

Timeocean (LST)

(a)

(b)

(c)

(m)

(m)

Figure 7. Decorrelation length (m) in the zonal (x, solid) and meridional (y,dashed) directions of (a) qt, (b) M and (c) S for different decay times. The timeon the bottom axis indicates the time (LST) in LAND and WET, whereas the axisat the top indicates the time (LST) in OCEAN.

of 1 km, a downdraught speed of 1 m s−1, a radius of 10 km anda typical propagation speed of 5 m s−1), longer than the ∼2500 sfound in OCEAN (with a typical cloud-base height of 500 m, adowndraught speed of 1 m s−1 a radius of 2 km and a typicalpropagation speed of 1 m s−1). Thus more of the tracer couldhave decayed before reaching the edge. Finally the decorrelationdistances are, as expected, longer for longer decay times.

Looking more closely at the evolution of D in Figure 7, Dof qt in the y direction shows a first pronounced maximum inLAND and WET at 0730 LST. This happens presumably when theinitial random perturbation has faded out and the field becomesvery homogeneous. Values then decay to a value of 500 m inthe forenoon hours. This corresponds to two grid points. In theafternoon, when the flow organizes,D increases to values of 8 km.For M, D increases in the afternoon up to a length of 15 km. Incontrast, D of S shows an early peak, presumably caused by a



LAND

(m)

(m) (m)

(m–1) (m–1)

(m–1)

S(k

) (k

g2 kg

–2 m

–1)

S(k

) (k

g2 kg

–2 m

–1)

S(k

) (m

3 s

–2 )

S(k

) (k

g2 kg

–2 m

–1)

(m–1)

(m)

(a) (b)

(c) (d)

Figure 8. Power spectral density of (a) qt, (b) w, (c) M and (d) S in LAND τ7200 and WET at 1300 LST (solid) and 1700 LST (dashed) and OCEAN at 0000 LST(solid) and 0700 LST (dashed) on the second day. Spectra are computed by applying a 2D Fourier transform layerwise on the 3D fields between 10 and 490 m in(a,c,d), and between 20 and 500 m in (b). The 2D spectra are averaged over annuli of equal wavenumber in spectral space. Spectra from the 25 vertical levels are finallyaveraged. Spectra are normalized by the total variance of the respective variable.

homogenization of the field, followed by a rapid decay to valuesof 250 m at 0800 LST, which is equal to one grid spacing. As forqt, the organization of the flow field in the afternoon increasesD. The spatial organization of qt and S show a rather similarpattern, which suggests that they are subject to the same emittingor organization process, whereas M shows a different patternwith an earlier and more pronounced increase in D. It appearsthat M is primarily distributed by the cold pool, whereas S ismainly emitted in the moist regions. S stems only to a minordegree from the interior of the cold pool. As the cold pools grow,qt and S are displaced further outside. This is confirmed lookingat the location of the emitting processes in Figure 3(c). As a result,D of M increases due to the spreading and growth of the coldpool in the afternoon, whereas D of qt and S increase in line withthe moist-patch region.

WET generally shows a comparable pattern but displaysan earlier evolution of the signal, in accordance with theearlier formation of clouds and precipitation. D of M isenhanced compared to LAND, in line with higher domain-meanevaporation rates and larger cold pools. On the other hand, D ofS grows to magnitudes very similar to LAND.

Calculated two-dimensional spectra (Figure 8) give a similarpicture. As the simulations start from homogeneous conditionsand there is no larger-scale information travelling into the modeldomain, total variance builds up over time and grows fromthe smallest resolved to larger scales. In all the simulations thegrowth results from the organization of precipitation throughcold pools, (e.g. Seifert and Heus, 2013). In LAND and WET, thisgrowth continues to larger scales than in OCEAN for all variablesconsidered. This is especially pronounced in w (Figure 8(b)).



Table 1. Fraction (%) of respective tracer contributing to qt for the different conditionally sampled regions and cases averaged between 1430 and 1800 LST in LAND,1200 and 1800 LST in WET and 0000 and 0700 LST in OCEAN.

LAND WET OCEAN

τ3600 τ7200 noτ τ7200 τ7200

M S M S M S M S M S

Active clouds 0.51 3.73 1.07 6.84 3.13 18.05 1.52 6.74 0.31 3.15Moist patches 2.60 7.03 4.21 10.50 8.11 21.76 4.29 9.05 0.90 3.98Cold pools 4.93 2.64 6.52 4.48 9.80 12.42 6.79 4.74 1.63 1.42

For moist patches and cold pools, M and S correspond to M and S . Active clouds are defined as those clouds where w >1 m s−1 and the cloud liquid water mixingratio exceeds 1.0×10−6 kg kg−1.

Time (LST) Time (LST) Time (LST) Time (min)

(a) (b) (c)

(e) (f) (g)

(d)

Figure 9. Anomalies of qt (solid black), S (solid grey), M (dashed grey) and the sum of S and M (black dashed) (kg kg−1) (a) at cloud-base height in active clouds,(b) in cold pools and (c) in moist patches for LAND using τ7200. The anomaly is calculated with respect to the value at the same grid point 1 h earlier. Panel (d) showsthe build-up over time of �qt (solid black), S (solid grey), M (dashed grey) and the sum of S and M (black dashed) averaged over all moist-patch regions withrespect to the value at the same grid point at 1300 LST. Zero on the minute axis corresponds to 1400 LST. (e–g) are as (a–c) respectively, but averaged between 1430and 1800 LST in LAND, 1200 and 1800 LST in WET, and 0000 and 0700 LST in OCEAN. For moist-patch and cold-pool regions, qt, M and S anomalies correspondto qt, M and S anomalies.

WET displays a very similar pattern to LAND but with anearlier upscale growth than LAND, in line with the earlierdevelopment of precipitation. The peak of the signal indicatingthe length-scale that contains most variance is located at longerwavelengths (smaller wavenumbers) in LAND than in OCEAN.The spectra of qt also show a pattern that is more similar tothe one of S than of M. M especially shows variance at longerwavelengths. The spectra of the evaporation processes itself donot show this variance at longer scales (not shown), whichconfirms the perception that the distribution of M is controlledby the spreading of the cold pool and thus shows a signal atlonger wavelengths. The resemblance of the spectra of qt and Ssubstantiates the view that S is emitted in places where qt is high.

5.2. Tracer anomalies

To further evaluate the importance ofM andS for the subsequentcloud development and their contribution to qt in the moistpatches, their values inside cold pools, moist patches and at cloudbases are quantified and documented in Table 1. The overallcontribution of the additional tracers to qt is small, which wouldsuggest that most moisture making up moist patches and cloudsstem from old, unlabelled moisture already present in the sub-cloud layer. The contributions of M and S are larger in LANDthan in OCEAN since both evaporation of precipitation and latent

heat fluxes are larger. Moreover the contribution increases forincreasing decay times for all areas and tracers considered.

The important quantity to look at is actually not thecontribution of M and S to qt but to its anomaly. Figure 9shows the qt, M and S anomaly both at cloud-base height andin cold pools and moist patches. At cloud-base height M, Sand qt are investigated, whereas in cold-pool and moist-patchregionsM, S and qt are evaluated. The anomaly is defined via therunning difference in the quantity considered over the last hour.A conditional sampling of the quantity considered over activeclouds, cold pools or moist patches is done at each point t0 in time,and the difference between the quantity at these points betweent0 and t0 − 1 h is computed. The conditional sampling is beingfixed over this last hour. Thereby, the build-up of the qt anomalyat a specific point, and the amount of M and S accountingfor it, can be isolated. Figure 9(d) illustrates this build-up at alllocations identified as moist patches from 1300 to 1400 LST inτ7200. The rightmost point of this panel corresponds to the pointat 1400 LST in Figure 9(c). At the base of active clouds, S and Mdisplay a small but steady contribution to the positive anomalyin qt (Figure 9(a)). In cold-pool regions the pattern varies overtime, with a distinct positive contribution ofM between 1200 and1800 LST (Figure 9(b)). The contribution of S decreases over timein moist-patch regions, whereas the contribution of M increases(Figure 9(c)). Analogous to the analysis of the budget terms in



section 4, the results from Figure 9(a–c) have been averaged intime between 1430 and 1800 LST in LAND, between 1200 and1800 LST in WET, and between 0000 and 0700 LST in OCEANand are displayed with the results from the other simulations in(e–g). Not surprisingly, the fraction of the qt anomaly that canbe explained by S and M increases for longer lifetimes of τ .In the places where active clouds occur (Figure 9(e)), 18% arecovered by the tracers in τ3600, 28% in τ7200 and 78% in noτ .In the moist patches (Figure 9(g)), 37% of the moisture anomalyis covered by S and M in τ3600, 55% in τ7200 and a completereplacement of unlabelled, ‘old’ moisture occurs in noτ . In τ7200the contribution of S to the qt anomaly in the moist patches is33%, whereas the contribution from M is only 21%. This meansthat, for a reasonable decay time, in the order of the lifetimeof a convective cell, the sgs surface fluxes and evaporation ofprecipitation can explain only half of the moisture, the other halfrepresenting old moisture previously present in the sub-cloudlayer. This remains true in WET, where both the anomaly of qt

and M are reduced, resulting in a similar concentration. On theother hand, S is reduced in WET compared to LAND, which canbe understood by a smaller saturation deficit in the moister sub-cloud layer. In OCEAN, a larger portion of �qt can be attributedto the emitted tracers: 56% at cloud base and 72% in moist-patchareas. Averaged between 0000 and 0700 LST, M accounts for22% of the qt anomaly in moist patches, whereas S has a share of50%. The qt anomaly, including S , is negative in the cold-poolregions, whereasM still shows increases there. This indicates thatM replaces ‘old’ sub-cloud layer moisture in this case whereasS is transported away by the cold-pool wake. This is observed inLAND, WET, and OCEAN.

Figure 9 also shows that S is larger than M in the moist-patch areas, and S is larger than M at cloud-base height atactive-cloud locations. These results are in contrast with thefindings of Tompkins (2001) who interpreted the water vapourin the moist rings around the cold pools to originate solely fromthe evaporated rain. Nevertheless using tracers reveals that theevaporated water makes up only a small portion of the moisturein the moist patches. Of course, M is larger than S inside coldpools, as this is the place where rain evaporates. But in the moistpatches, most of the moisture has been inside the sub-cloudlayer before the cold pool hits and redistributes it. The ‘fresh’contribution originates mostly from the sgs surface fluxes. InOCEAN this surface portion is increased compared to LAND andWET, whereas the portion stemming from rain evaporation iscomparable to LAND. It seems that ‘fresh’ moisture from the seasurface is more readily reused in OCEAN than in LAND since itis distributed over a smaller area.

The analysis suggests that the sub-cloud layer is constantlymoistened by sgs surface moisture fluxes and to a minor degreeby the evaporation of rain. These fluxes are strongly modulatedby cold-pool dynamics. The moisture present in the sub-cloudlayer is quickly redistributed by the flow field induced bythe cold pools. Cold-pool dynamics thus influence both themoistening and the redistribution process. With wind and thewind shear, the evaporation occurs over larger spatial scales,which distributes M over larger scales. Moreover in LAND,evaporation rates are larger leading to more intense cold poolsfeaturing an edge travelling further distances. This leads to anadditional dilution of bothM andS but to a stronger localizationof ‘old’ qt.

We can only speculate about the recycling rate, but it appearsthat the moisture is more readily reused in OCEAN than inLAND. The longer the decay time for the labels, the more sub-cloud layer moisture will be labelled, until at some point the entiremoisture will have originated from either sgs surface moisturefluxes or evaporation. Of course this conclusion is valid onlyin our closed framework, whereas in an atmosphere subject tolarge-scale moisture advection, the latter would constitute anadditional source for moisture.

6. Conclusions

Under the overarching question of the origin of moisture fordeep convection, this study has investigated moisture pathwaysfor convective clouds in the absence of large-scale forcing fora continental and oceanic case. The generality of the resultswas further tested in a modified continental case which holdslarger rain amounts. In this set-up, turbulence, surface fluxes,evaporation of precipitation and advection related to cold-pooldynamics are the potential mechanisms responsible for moisturemodifications in the sub-cloud layer. To identify the dominantprocess, the moisture budget was investigated. This was done forthe entire domain, and separately for cold-pool regions and moist-patch regions. Moist patches are regions where qt is enhanced andwhich serve as a preferred location for cloud formation. Moistureadvection is identified as the overwhelming contributor to thetemporal evolution of qt in the cold pools and moist patches,followed by surface moisture fluxes and a small contributionfrom rain evaporation. Thereby, the cold pools are dried bythe divergent wind field, whereas rain evaporation and sub-gridscale (sgs) moistening is increased compared to domain-averagedvalues. On the other hand, in the moist-patch regions the pictureis reversed with increased moisture convergence but reducedrain evaporation and sgs fluxes. Splitting up advection into itshorizontal and vertical contributions reveals that cold pools aredried by horizontal moisture flux divergence, which is partlycompensated by a converging downward moisture flux. Moistpatches show the opposite picture with horizontal advectionposing a strong positive contribution which is partially balancedby vertical advection. Advection contributes 86%, sgs fluxes 11%and evaporation 4% to the qt tendency in moist patches in theland case, whereas in the ocean case advection contributes to125%, sgs fluxes to −32% and evaporation to 7%. Thus, even inthe absence of large-scale processes, local advection of moistureappears as a leading player in feeding convective clouds.

A further insight into the origin of the moisture was gainedby analysing additional scalars which label air masses which havegained qt from evaporation of rain or surface moisture fluxes.These scalars revealed that rain evaporated in the cold pools ispushed outwards in a shallow layer close to the surface by thecold-pool wakes. The emission of moisture from the surface isenhanced in the moist regions. In combination with a transport ofmoisture originating from the surface inside the cold pools by thecold-pool wakes, this leads to an accumulation of surface moisturein narrow regions around the cold pools. The moisture anomalyin the moist patches consists of 33% of moisture stemming fromthe surface in LAND and 50% in OCEAN, and to a minor degreefrom rain evaporation (21% in LAND and 22% in OCEAN).Old moisture already present in the sub-cloud layer (and is thusunlabelled) makes up 46% of qt in LAND and 28% in OCEAN.The longer the memory of the tracers, the larger the portion ofthe moisture anomaly that can be explained by the additionaltracers. The overall findings hold both for two cases of convectiondevelopment over land which differ in their precipitation amountand a case over ocean. In the ocean case, the contribution of thesurface moisture fluxes to the advected moisture is about 50%larger than over land.

We can only speculate how the results would change under theinfluence of large-scale moisture advection. It depends strongly onthe height at which the maximum advection is located. In the caseof mid-tropospheric moistening, this will presumably mostly aidthe convective clouds to deepen by reducing dry-air entrainment.This in turn will enhance precipitation, an enhanced release ofM and cold-pool formation, leading to an enhanced release of S ,larger moist patches and finally to a positive feedback with largerand deeper clouds. The amplitude of the moisture perturbationinside the moist patches would supposedly also increase. In thecase of a moistening of the sub-cloud layer, more qt can belocalized and the lifted condensation level drops, whereas bothevaporation of rain and surface moisture fluxes will be decreased.



The question of whether �qt or �S increases more stronglywould determine if the cloud formation mechanism becomesmore similar to LAND or OCEAN.

Acknowledgements

This research was carried out as part of the Hans Ertel Centrefor Weather Research. This research network of Universities,Research Institutes and the Deutscher Wetterdienst is fundedby the BMVI (Federal Ministry of Transport and DigitalInfrastructure). We want to thank the participants of the COSTAction ES0905 meeting on cold pools for laying the initialcornerstone for the study.

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