Problem Session (afternoon, 9/19/11)

•  CCN growth; supersaturation in a updraft (finish up last few slides from Lecture 12)

•  Atmospheric Aerosols (2 page notes + spreadsheet)

•  Computing CCN spectra (spreadsheet)

LCL  

LFC  

Figure 1: Skew-T Ln-P plot from Dodge City, KS at 0000 UTC on 15 September 2004

Surface  moisture  content  ~  10  g/kg  (water  vapor  per  dry  air)  

Here  air  can  hold  only~  8  g/kg  2  g  want  to  condense;  S  >  1  if  sFll  in  vapor  

We  used  this  slide  to  discuss  where  RH=100%  (S=1)  and  how  real  clouds  “overshoot”  and  produce  S  >  1,  because  CCN  generally  cannot  acFvate  at  S=1  AND  condensaFon  takes  Fme  (drop  growth  equaFon)  

Consider the growth of a population of droplets

In clouds many droplets grow at the same time (on activated CCN). Typical concentrations may be a few hundred per cm3 in maritime clouds and ~500-700 cm-3 for continental clouds. These droplets compete for available H2O vapor made available by condensation associated with the rising air parcels. This of course creates a supersaturation which is reduced by condensational growth on the cloud droplets.

Time rate of change of supersaturation,

supersaturation

condensational growth rate

saturation mixing ratio; updraft velocity

where is the droplet concentration, assumed to be

Net rate of change = rate of production of supersaturation – rate of consumption (by condensation)

cloud droplet concentration determined

2) drop growth maximum around Smax

3) smallest particles become haze droplets

4) Activated droplets become monodisperse in size

INITIAL RADII α salt mass radii

1) Max supersaturation achieved few tens of meters above cloud base

Increasing salt mass

non-activated droplets

Activated droplets

MONODISPERSE 0 6 60

Back to our problem session (9/16/11) ATS 620 F11 Lecture 11: Calculations of aerosol and CCN distributions 16 September 2011 1. Finish discussion of CCN measurements (in PPT for Lecture 10) 2. Köhler calculation spreadsheet

a. review input / output fields b. review equations used to compute the curve c. plotting: using x-y scatterplot feature d. finding zeroes: setting up and using Goal Seek e. solve the following:

For a particle with !=0.1 (typical atmospheric organic particle), compute the Köhler curves and critical supersaturations for activation for particles with dry diameters of 0.01, 0.1, and 0.5 !m. How sensitive is the calculation to the choice of temperature? If the organic has surfactant properties and reduces surface tension by 20%, how much do the critical supersaturations change? As you work on the calculations, take notice of:

- what is the water activity close to activation for the various dry particle sizes? - how big / small does the Kelvin effect become over the range of wet sizes used?

3. Kappa lines sheet a. review the matrix of variables

4. Discuss the writeup on lognormal distributions. 5. Size distribution calculation spreadsheet

a. review input fields b. review equations used to compute the curves c. estimating number concentrations within bins, and cumulative concentrations

6. Calculation of cumulative CCN distribution The goal of this problem is to generate curves similar to the one shown on page 30 of Lecture 10 (Andreae and Rosenfeld, 2008, summarizing published data). The y axis is cumulative CCN number concentration, in particles cm-3, and the x axis is critical supersaturation in percent. Compute such a curve for an aerosol that is mostly organic, with !=0.1, and having a lognormal number distribution with dpg = 0.1 !m, "g = 1.8, and N = 500 cm-3. There are probably a number of ways to approach this. In class we will brainstorm to come up with several options. You will certainly need the size distribution worksheet, and think about using the kappa lines sheet as well.

Start here

The lognormal aerosol size distribution Aerosols are described in terms of their frequency function, where the fraction of particles, df, having diameters between dp and dp + ddp is

!

df = f (dp )ddp

f (dp ) =dfddp

Note that the value of f(dp) at a particular dp does not have physical meaning, but the area under the curve between any two values of dp does. For example, if we are considering a number size distribution,

!

f (dp ) =dNddp

N1 =dNddp

d p =0.1µm

"

# ddp

where N1 is the total number concentration of particles having diameters larger than 0.1 !m. Because the range of particle diameters (the x-axis values) is so large for the atmospheric aerosol, we usually use ln dp in place of dp. Further, the distributions of atmospheric aerosols typically exhibit Gaussian (normal) shapes when the x variable is chosen as ln dp. So data are generally fit to lognormal distributions:

!

f (ln dp ) =dN

d ln dp

=N

2" ln# g

exp $(ln dp $ ln dpg )

2

2(ln# g )2

%

& '

(

) *

The Gaussian’s midpoint diameter (geometric median) is dpg. The spread of the distribution is given by !g, where !g =1 is for monodisperse aerosol. N is the total number concentration. The 3 parameters fix the shape and position of the distribution in diameter space. All functions derived from the lognormal (e.g., number distribution, surface area distribution, volume or mass distribution) are also lognormal. Simple relationships relate the median diameters of the various distributions and all have the same !g.

Discussed this sheet in workbook – calculate and plot number and mass distributions (aerosols ; CAN apply to drop size distributions if lognormal “fits” data)

Pruppacher  and  KleU,  1978  

•  ConFnental  air  masses  are  richer  in  CCN  than  mariFme  air  masses.  

•  ConcentraFons  of  CCN  increase  with  supersaturaFon.  

•  Some  ocean  measurements  are  influenced  by  conFnents.    

•  Remote  ocean  regions  have  the  lowest  CCN  concentraFons.  

•  At  1  %  SS,  N  is  about  1000  cm-­‐3  for  conFnental  air  masses.  

•  At  1%    SS,  N  is  about  100  cm-­‐3  for  mariFme  air  masses.  

RelaFonship  between  CCN  and  supersaturaFon  S  can  be  expressed  as  a  power  law  of  the  form  

                                                             Nccn  =  cSk                typical  units  are  cm-­‐3,  where  S  is  supersaturaFon  in  percent.  

ConFnental  air  masses,      c  =  600  cm-­‐3,  k  =  0.5  MariFme  air  masses,              c  =  100  cm-­‐3,  k  =  0.7  

Reflects  “classic”  picture  –  before  recent  development  of  

commercial  instrument  

Andrea  and  Rosenfeld,  Earth  Science  Reviews,  

89  (2008),  13-­‐41.      

Last  problem  discussed:  Why  do  these  lines  have  this  shape?  Which  parFcle  acFvate  “first”  (at  the  lowest  sc)  in  the  cumulaFve  CCN  concentraFons  shown  here?  

If  we  compute  the  cumulaFve  CCN  concentraFon  for  a  lognormal  aerosol  (with  a  chosen  kappa),  do  we  get  something  that  looks  like  this,  or  that  can  be  fit  with  the  power  law  on  the  previous  slide?  

Approaching the problem

•  Choose kappa = 0.1 (see problem statement) •  Make an array of particle sizes

•  For each particle size, find critical supersaturation

•  How many particles are there in the distribution, LARGER than this size (because those will have the lower sc and will activate before this size, and we’re accumulating all of the particles that can activate up to that particular sc )

11  

Power  law  fit?