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)
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) Here air can hold only~ 8 g/kg 2 g want to condense; S > 1 if sfll in vapor LFC LCL Surface moisture content ~ 10 g/kg (water vapor per dry air) Figure 1: Skew-T Ln-P plot from Dodge City, KS at 0000 UTC on 15 September 2004
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 cm 3 in maritime clouds and ~500-700 cm -3 for continental clouds. These droplets compete for available H 2 O 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, Net rate of change = rate of production of supersaturation rate of consumption (by condensation) supersaturation condensational growth rate saturation mixing ratio; updraft velocity where is the droplet concentration, assumed to be
INITIAL RADII α salt mass radii 0 6 60 MONODISPERSE Activated droplets Increasing salt mass non-activated droplets 1) Max supersaturation achieved few tens of meters above cloud base cloud droplet concentration determined 2) drop growth maximum around S max 3) smallest particles become haze droplets 4) Activated droplets become monodisperse in size
Back to our problem session (9/16/11) ATS 620 F11 Lecture 11: Calculations of aerosol and CCN distributions 16 September 2011 Start here 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 d pg = 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.
The lognormal aerosol size distribution Aerosols are described in terms of their frequency function, where the fraction of particles, df, having diameters between d p and d p + dd p is df = f (d p )dd p f (d p ) = df dd p Note that the value of f(d p ) at a particular d p does not have physical meaning, but the area under the curve between any two values of d p does. For example, if we are considering a number size distribution, f (d p ) = dn dd p N 1 = " dn # dd p dd p d p =0.1µm where N 1 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 d p in place of d p. Further, the distributions of atmospheric aerosols typically exhibit Gaussian (normal) shapes when the x variable is chosen as ln d p. So data are generally fit to lognormal distributions: f (ln d p ) = dn d ln d p = N % exp $ (ln d $ ln d p pg ) 2 ( ' * 2" ln # g & 2(ln# g ) 2 ) The Gaussian s midpoint diameter (geometric median) is d pg. 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. Reflects classic picture before recent development of commercial instrument RelaFonship between CCN and supersaturafon S can be expressed as a power law of the form N ccn = cs k 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
Last problem discussed: Why do these lines have this shape? Which parfcle acfvate first (at the lowest s c ) 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? Andrea and Rosenfeld, Earth Science Reviews, 89 (2008), 13-41.
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 s c and will activate before this size, and we re accumulating all of the particles that can activate up to that particular s c ) Power law fit? 11