FINE-SCALE MODELING OF ENTRAINMENT AND MIXING OF CLOUDY AND CLEAR AIR Steven K. Krueger * University of Utah, Salt Lake City, Utah, USA 1. INTRODUCTION The EMPM (Explicit Mixing Parcel Model) pre- dicts the evolving in-cloud variability of tempera- ture and water vapor mixing ratio due to entrain- ment and finite-rate turbulent mixing using a 1D representation of a rising cloudy parcel (Krueger et al. 1997). The 1D formulation allows the model to resolve fine-scale variability down to the small- est turbulent scales (about 1 mm). The EMPM calculates the growth of thousands of individual cloud droplets based on each droplet’s local envi- ronment (Su et al. 1998). How do entrainment and mixing affect droplet spectral evolution in the EMPM? The following sequence of the events is illustrated in Fig. 1 for an isobaric entrainment and mixing event. The parcel first ascends adiabatically above cloud base, while the droplets grow by condensation. When entrainment occurs, the subsaturated entrained air replaces a a same-sized segment of the cloudy parcel. The cloudy air and the newly entrained air undergo a finite rate turbulent mixing process. During this process, many droplets encounter the entrained subsaturated air, resulting in partial or even total evaporation of some droplets. We used the EMPM to investigate the impact on droplet spectra evolution in cumulus clouds of the following aspects of entrainment and mixing: Parcel trajectory after entrainment: Isobaric versus ascending. Entrained CCN concentration: Zero, half cloud base concentration, or full cloud base concentration. We were motivated by aircraft measurements in cumulus clouds of cloud droplet number concen- tration (N ) and mean volume radius (r v ), aver- * Corresponding author address: Department of Meteorology, University of Utah, Salt Lake City, UT 84112. E-mail: [email protected]droplet evaporation molecular diffusion turbulent deformation saturated parcel entrainment Figure 1: A parcel undergoing isobaric mixing is represented by a 1D domain in the EMPM. The parcel’s internal structure evolves due to dis- crete entrainment events and turbulent mixing (turbulent deformation and molecular diffusion). Droplets evaporate based on each droplet’s local environment. aged over 10-m intervals, normalized by their adi- abatic values, and plotted on a diagram with co- ordinates N/N a and V/V a = r 3 v /r 3 va . The prod- uct of the coordinates is the LWC normalized by its adiabatic value. Such a diagram (from Bur- net and Brenguier 2007) for cloud traverses about 1500 m above cloud base for a case during SCMS (Small Cumulus Microphysics Study) is shown in Fig. 2. The challenge is to explain the observed distributions. Burnet and Brenguier proposed that isobaric
Transcript
FINE-SCALE MODELING OF ENTRAINMENT AND MIXING OF CLOUDY AND CLEAR AIR
Steven K. Krueger∗
University of Utah, Salt Lake City, Utah, USA
1. INTRODUCTION
The EMPM (Explicit Mixing Parcel Model) pre-dicts the evolving in-cloud variability of tempera-ture and water vapor mixing ratio due to entrain-ment and finite-rate turbulent mixing using a 1Drepresentation of a rising cloudy parcel (Krueger etal. 1997). The 1D formulation allows the modelto resolve fine-scale variability down to the small-est turbulent scales (about 1 mm). The EMPMcalculates the growth of thousands of individualcloud droplets based on each droplet’s local envi-ronment (Su et al. 1998).
How do entrainment and mixing affect dropletspectral evolution in the EMPM? The followingsequence of the events is illustrated in Fig. 1 foran isobaric entrainment and mixing event. Theparcel first ascends adiabatically above cloud base,while the droplets grow by condensation. Whenentrainment occurs, the subsaturated entrainedair replaces a a same-sized segment of the cloudyparcel. The cloudy air and the newly entrainedair undergo a finite rate turbulent mixing process.During this process, many droplets encounter theentrained subsaturated air, resulting in partial oreven total evaporation of some droplets.
We used the EMPM to investigate the impacton droplet spectra evolution in cumulus clouds ofthe following aspects of entrainment and mixing:
Parcel trajectory after entrainment: Isobaricversus ascending.
Entrained CCN concentration: Zero, halfcloud base concentration, or full cloud baseconcentration.
We were motivated by aircraft measurements incumulus clouds of cloud droplet number concen-tration (N) and mean volume radius (rv), aver-
∗Corresponding author address: Department ofMeteorology, University of Utah, Salt Lake City, UT 84112.E-mail: [email protected]
droplet evaporation
molecular diffusion
turbulent deformation
saturated parcel
entrainment
Figure 1: A parcel undergoing isobaric mixingis represented by a 1D domain in the EMPM.The parcel’s internal structure evolves due to dis-crete entrainment events and turbulent mixing(turbulent deformation and molecular diffusion).Droplets evaporate based on each droplet’s localenvironment.
aged over 10-m intervals, normalized by their adi-abatic values, and plotted on a diagram with co-ordinates N/Na and V/Va = r3
v/r3va. The prod-
uct of the coordinates is the LWC normalized byits adiabatic value. Such a diagram (from Bur-net and Brenguier 2007) for cloud traverses about1500 m above cloud base for a case during SCMS(Small Cumulus Microphysics Study) is shown inFig. 2. The challenge is to explain the observeddistributions.
Burnet and Brenguier proposed that isobaric
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Figure 8 (continue).
b)
Figure 2: N -V diagram from SCMS for 10 August1995. Plotted are 909 cloud samples, each of 10-m length. From Burnet and Brenguier (2007).
mixing, combined with buoyancy sorting, can ex-plain the the observed distributions of N and rv
in cumulus clouds. However, we propose that ad-ditional processes (ascent of entrained air and en-trainment of CCN) are likely to be important.
To explore the range of potential N -V distribu-tions that might be encountered in cumulus cloudsand to relate them to cloud processes, we appliedthe EMPM to a variety of realistic entrainmentand mixing scenarios. The consequences of par-cel trajectory after entrainment (isobaric versusascending), and entrained CCN concentration onN -V distributions in entraining, non-precipitatingcumulus clouds as predicted by the EMPM are pre-sented in Section 2. Conclusions follow in Section3.
2. ENTRAINMENT AND MIXING IN THEEMPM
2.1 Isobaric mixing
Figure 3 shows the sequence of states involvedin isobaric mixing in the EMPM after an entrain-ment event. The states are numbered from 1 to4. State 1 is the result of adiabatic ascent fromcloud base. The variability of the droplet num-ber concentration at this time is due to the small
number of droplets (about 100) in each 1-m seg-ment. State 2 is due to the initial breakdown ofthe entrained blob into smaller segments, with lit-tle droplet evaporation. This reduces N and LWCby dilution, but does not decrease rv.
Between states 2 and 3, droplets evaporate untillocal saturation is achieved. This reduces the localrv, but does not change the local N unless somedroplets totally evaporate. In this case, almost nodroplets totally evaporate. The blue line is theso-called ”homogeneous” mixing line. It indicatesall possible values of (N ,V ) in saturated mixturesof entrained and adiabatic (undiluted cloud-base)air in which no droplets have totally evaporated.1 Therefore, the N -V distribution moves down-wards towards the blue line between states 2 and3. In state 3, all mixtures are again saturated,due to droplet evaporation. The rate at which theadjustment to saturation occurs is limited by therate of turbulent mixing in this case.
Between states 3 and 4, the resulting saturatedparcels mix. Because the blue line is also a mixingline for saturated parcels, the N -V distributionconverges towards its domain average. In state 4,the parcel is once again statistically uniform.
Burnet and Brenguier used a simple mixingmodel to demonstrate that isobaric entrainmentand mixing events can produce (N , V ) pairsanywhere on the diagram between the ”homoge-neous” mixing line and N = 0. This result agreeswith the EMPM results shown in Figure 3.
Figure 4 conceptually illustrates the sequence ofstates involved in isobaric mixing after an entrain-ment event for two parcels based on the analysisof EMPM results such as those shown in Fig. 3.The entrained air fraction is greater for the “blue”parcel (0.5) than for the “red” parcel (0.3). As aresult, the LWC of the “blue” parcel is less thanthat of “red” parcel, both immediately after en-trainment (state 2), and after saturation adjust-ment (state 3). In this case, no droplets totallyevaporate, so the state 3 N − V coordinates forboth parcels lie on the same mixing line. Mixingbetween these the two parcels produces state 4,
1For entrainment into cumulus clouds, the mixing linedepends primarily on the relative humidity (RH) of the en-trained air.
Figure 2: N -V diagram for isobaric mixing in the EMPM after an entrainment event. Each point is a 1-m average.Plotted in each panel are points from 11 “traverses” of the 80-m EMPM domain during an 8.25-s interval. Time increasesclockwise from the upper left panel.
evaporate. The blue line indicates all possible values of(N ,rv) in saturated mixtures in which no droplets have to-tally evaporated. Therefore, the N -rv distribution movesdownwards towards the blue line during the second stage.
During the third stage (panels 5 and 6), the resultingsaturated parcels mix. Because the blue line is also a mixingline for saturated parcels, the N -rv distribution convergestowards its domain average during this stage.
Figure 3 presents the distributions of the domain aver-ages of two EMPM simulations of isobaric mixing in a 20-mdomain with 7 sequential entrainment events. In this case,the domain averages are completey determined by the en-trained air properties (entrainment fraction and RH), andindicate nothing about the mixing process. Note that en-trained CCN have no impact when the mixing is isobaric.
2.2 Ascent with and without entrained CCN
The two plots in Fig. 4 show the dramatic impact of en-trained CCN in an ascending parcel (80-m domain) with se-quential entrainment events. Without entrained CCN (leftpanel), r3
v grows to 150 percent of adiabatic at the high-est level (1500 m above cloud base), while N decreasesto 25 percent of adiabatic (”weed and feed”). When CCNare entrained at cloud base concentrations (right panel), r3
v
decreases to about 40 percent of adiabatic, while N onlyslightly decreases, to about 90 percent of adiabatic (”weed,seed, and feed”).
Figure 5 shows the time series of all 10-m averages foran EMPM simulation in a 200-m domain without entrainedCCN. Compared to the domain-averaged results, the 10-m
averages are much more variable (and realistic) because theentrained air fraction in each 10-m segment is determinedby the EMPM’s stochastic mixing process, rather than be-ing specified. As a result, the 10-m averages from the200-m domain results can be directly compared to aircraftmeasurements, such as those shown in Fig. 1.
Figure 6 shows the time series of all 10-m averages foran EMPM simulation in an 80-m domain with entrainedCCN at one half of cloud base concentrations, while Fig.7 shows the same for an EMPM simulation with entrainedCCN at cloud base concentrations.
3. CONCLUSIONS
These (and other) comparisons between EMPM resultsand observations indicate that without entrained CCN, rv istoo large and N is too small, and suggest that distributionsof N and rv similar to those observed can be produced in anascending parcel by entraining air with intermediate CCNconcentrations.
ACKNOWLEDGMENTS. This material is based upon worksupported by the National Science Foundation under GrantNo. ATM-0346854.
REFERENCES
Burnet, F., and J.-L. Brenguier, 2006: Observational studyof the entrainment-mixing process in warm convectiveclouds J. Atmos. Sci., accepted.
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Figure 3: N -V diagram for isobaric mixing in the EMPM after an entrainment event. Each point is a1-m average. Plotted in each panel are points from 11 “traverses” of the 80-m EMPM domain duringeach 8.25-s interval ending at the indicated time.
Figure 4: Entrainment and isobaric mixing for two parcels. No droplets totally evaporate.
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which also lies on the mixing line.Figure 5 is like Fig. 4 except that in this
case some droplets completely evaporate betweenstates 2 and 3, so that N decreases after en-trainment. If V does not change during evapora-tion, the process is called “extreme inhomogenousmixing, and each droplet either completely evap-orates, or does not evaporate at all. As before,the parcel is saturated with LWC = NV when itreaches state 3.
Morrison and Grabowski (2008) proposed thefollowing general relationship betwen Nf , the fi-nal droplet concentration after turbulent mixingand evaporation, and Ni, the droplet concentra-tion after entrainment (for a parcel model) or aftertransport (for an Eulerian grid volume):
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Figure 6: Time sequence of domain averages forisobaric mixing in the EMPM (80-m domain) af-ter 7 sequential entrainment events. The mixingparameter α is given for each entrainment event.
each mixing scenario in Fig. 5, and for each en-trainment and isobaric mixing event in the EMPMsimulation shown in Fig. 6. The results suggestthat, for given entrained air properties and mixingtime scale, α increases as the LWC decreases.
Schluter (2006) analyzed a set of more than 100EMPM simulations of entrainment and isobaricmixing that covered a wide range of entrained airproperties and mixing time scales. We have usedher results to calculate α for each of the EMPMsimulations. We anticipate that further analyis ofher results will provide some guidance for param-eterizing α in cloud-resolving models that do notresolve the entrainment and mixing process.
2.2 Ascent with and without entrained CCN
Figure 7 presents the distributions of the do-main averages of two EMPM simulations of iso-baric mixing in a 20-m domain with 7 sequen-tial entrainment events. One had no entrainedCCN, while the other entrained CCN. Note thatentrained CCN have no impact when the mixingis isobaric.
The two plots in Fig. 8 show the dramatic im-pact of entrained CCN in an ascending parcel (80-m domain) with sequential entrainment events.Without entrained CCN (left panel), r3
Figure 7: Time sequence of domain averages for isobaric mixing in the EMPM (20-m domain) after 7sequential entrainment events. Left: No entrained CCN. Right: with entrained CCN.
Figure 8: Like Fig. 7 except for ascent in an 80-m EMPM domain.0.1
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Figure 9: Left: Entrainment, mixing, and condensation (C) for a parcel that ascends after each entrain-ment event but entrains no CCN. Right: Entrainment, mixing, activation (A), and condensation (C) fora parcel that ascends after an entrainment event that entrains CCN.
150 percent of adiabatic at the highest level (1500m above cloud base), while N decreases to 25percent of adiabatic. When CCN are entrainedat cloud base concentrations (right panel), r3
v de-creases to about 40 percent of adiabatic, whileN only slightly decreases, to about 90 percent ofadiabatic.
If a cloudy parcel ascends during entrainmentand mixing, the relative humidity of the entrainedair will increase, thereby shifting the mixing lineupwards and increasing the LWC (”feeding”). Ifno CCN are entrained and no droplets totallyevaporate, N will remain constant after entrain-ment, so that rv will also increase. This ”weedand feed” scenario is illustrated in the left panelof Fig. 9.
Due to ascent and adiabatic cooling, newly en-trained air may become supersaturated and someof the entrained CCN may be activated, therebyincreasing N (”seeding”) but decreasing rv (forconstant LWC). This ”weed, seed, and feed” sce-nario is illustrated in the right panel of Fig. 9.
Figure 10 shows the time series of all 10-m av-erages for an EMPM simulation in a 200-m do-main without entrained CCN. Compared to thedomain-averaged results, the 10-m averages aremuch more variable (and realistic) because the en-trained air fraction in each 10-m segment is deter-mined by the EMPM’s stochastic mixing process,rather than being specified. As a result, the 10-maverages from the 200-m domain results can bedirectly compared to aircraft measurements, suchas those shown in Fig. 2.
Figure 11 shows the time series of all 10-m aver-ages for an EMPM simulation in an 80-m domainwith entrained CCN at one half of cloud base con-centrations, while Fig. 12 shows the same for anEMPM simulation with entrained CCN at cloudbase concentrations.
3. CONCLUSIONS
Entrainment followed by isobaric mixing re-duces the droplet number concentration by di-lution (”weeding”) and the LWC and mean vol-ume radius by droplet evaporation. As long as nodroplets completely evaporate, the entrained air
fraction determines N , and mixtures of entrainedand adiabatic (undiluted cloud-base) air define theso-called ”homogeneous” mixing line on the N -r3
v
diagram.If a cloudy parcel ascends during entrainment
and mixing, the RH of the entrained air will in-crease, thereby shifting the mixing line upwardsand increasing the LWC (”feeding”). If N remainsconstant, rv will also increase. Due to ascent andadiabatic cooling, newly entrained air may becomesupersaturated and some of the entrained CCNmay be activated, thereby increasing N (”seed-ing”) but decreasing rv (for constant LWC).
These (and other) comparisons between EMPMresults and the observations of Burnet and Bren-guier (2007) suggest that distributions of N andV similar to those observed can be produced in anascending parcel by entraining air with intermedi-ate CCN concentrations.
ACKNOWLEDGMENTS. This material is basedupon work supported by the National ScienceFoundation under Grant No. ATM-0346854.
REFERENCES
Burnet, F., and J.-L. Brenguier, 2007: Observa-tional study of the entrainment-mixing processin warm convective clouds J. Atmos. Sci., 64,1995–2011.
Krueger, S. K., C.-W. Su, and P. A. McMurtry,1997: Modeling entrainment and fine-scalemixing in cumulus clouds. J. Atmos. Sci.,54, 2697–2712.
Morrison, H., and W. W. Grabowski, 2008: Mod-eling supersaturation and subgrid-scale mix-ing with two-moment bulk warm microphysics.J. Atmos. Sci., 65, 792–812.
Schluter, M. H., 2006: The Effects of Entrainmentand Mixing Processes on the Droplet Size Dis-tributions in Cumuli. M.S. Thesis, Universityof Utah, 92 pp.
Su, C.-W., S. K. Krueger, P. A. McMurtry, andP. H. Austin, 1998: Linear eddy modeling ofdroplet spectral evolution during entrainmentand mixing in cumulus clouds. Atmos. Res.,47–48, 41–58.
Figure 10: 10-m averages for an EMPM simulation in a 200-m ascending domain without entrainedCCN. Left: All values. Right: Values for a short time interval, similar to what would be sampled by anaircraft traverse.
