Simulating of Simulating of nucleation bursts nucleation bursts in forest in forest

Simulating of Simulating of

nucleation bursts nucleation bursts

in forest

in forest

Updates in the simulator:

• Improved submodel of the background aerosol sink.

• Dry deposition according to the

Churchill-Bernstein approximation.

• Minor technical improvements.

Both the exe-file and the Pascal source (Delphi console application) will be

available for everybody in September.

Time

Process in free air Process in forest Final status

Initial steady state Forest entrance

Nucleation period

Forest processing

Neutral nucleation

T = 0ºC, p = 1013 mb.

Z

= 1.36 cm

V

s

, Z

= 1.56 cm

V

s

,

 = 1.6×10

cm

s

,  = 2 g cm

.

I = 4 cm

s

, J

= 8 cm

s

, d

= 1.5 nm, no positive ion-induced nucleation.

First condensing substance: 0.55 nm, 2 g cm

, effective dipole polarizability 0.149 nm

, plain Knudsen growth rate 2 nm/h,

critical size and extra temperature of quantum rebound 2.5 nm and 600 K.

Second condensing substance: 0.8 nm, plain Knudsen growth rate 4 nm/h,

nano-Köhler threshold 3 nm and power 2.

Background aerosol: 200 nm and 1000 cm

. Forest: wind 1 m s

, air residence 200 s,

needle diameter 0.9 mm,

total length in a unit volume 200 m

.

Mixed nucleation: 75% neutral + 25% negative

The calculations were made with 3600 time steps and

2666 size sections

up to diameter of 10.7 nm.

Four runs required for generating the example data. The total

computing time was 41 s when adapted to a 1 GHz Pentium

processor.

Depletion of ions on large particles (old model)

 

 ^  _ ^{  }



















N N

q p p

p

q p p

p

d q d

D s

d q d

D s

2 2

D+ and D− are diffusion coefficients of ions, N is concentration of pre-existing particles of background aerosol, d

and q

, are the mean diameter and the algebraic mean charge number of aerosol particles.

d

is characteristic length of Coulomb attachment

kT d _q e

 

 4

2

 1.671×104 / (T : K) nm

where e is elementary charge, 

is electric constant,

k is Boltzmann constant, and T is absolute temperature.

Depletion of ions on large particles (new model)

 

 ^{ }  _ ^{  }





















N N

q p

p p

q p

p p

d cq

d D

s

d cq

d D

s

) nm 5

. 1 (

2

) nm 5

. 1 (

2

nm 23

nm 9



 

p p

d

c d

Eq. (7) = old approximation

Eq. (10) = new approximation

Useful subroutines in the Pascal source

function

Mobility

{velocity/force} (GasMass {amu}, { 28.96 28.02 } { (m/s) / fN } Polarizability {nm³}, { 0.00171 0.00174 } VisCon1 {nm}, { 0.3036 0.2996 } {JAS26, 1995} VisCon2 {K}, { 44 40 } {pp. 459-475} VisCon3, { 0.8 0.7 } {C: H.Tammet} Pressure {mb},

Temperature {K},

ParticleDensity {g cm^-3, for cluster ions typically 2.08}, ParticleCharge {e, for cluster ions 1}, MassDiameter {nm} : double) : double;

function

MassDiameter

{nm} (Pressure {mb}, Temperature {K},

ParticleDensity {g cm^-3, for cluster ions typically 2.08}, ParticleCharge {e, for cluster ions 1}, MechMobility {m fN^-1 s^-1} : real) : real;

{MechMobility = 0.624 * Z (cm²V^-1s^-1) / q (e)}

{Ion-particle attachment or coagulation coefficient}

function

beta

q, {number of charges on particle, attracting -, repelling +}

{cm³/s} di, {diameter of ion : nm}

gcm3, {ion density : g cm^-3, typically 2.08}

dp, {diameter of particle : nm}

T, {temperature : K}

p {pressure : mb} : double) : double;

{Uses external function "Mobility" (B: 1e15 m s^-1 N^-1), diameters of ions of mobility 1.36 and 1.56 cm²/Vs, are in standard conditions 0.79 and 0.70 nm}

{Particle-particle coagulation coefficient, Sahni approximation}

{Uses external function "Mobility"}

function

coag

d1, {diameter of small neutral particle : nm}

{cm³/s} d2, {diameter of large charged or neutral particle : nm}

h, {extra distance : nm, typically 0.115}

gcm3, {small particle density : g cm^-3, typically 1.5-2}

q, {large particle charge : e}

aa, {small particle polarizability : angstrom^3}

d0, {critical diameter of quantum rebound : nm, typical 2.5}

T0, {extra temperature of quantum rebound: K, typically 300}

T, {air temperature : K}

mb {air pressure : mb} : double) : double;

{Polarizability in angstrom^3 is often estimated as equal to the number of atoms in the cluster or as r^3 for large particles}

{Growth rate factor GR/GRo for the first substance,

designed as modification of function coag at non-evaporating condensation, GRo is plain Knudsen growth rate explained in (Tammet, Kulmala, 2005)}

function growthfactor1 ({dimensionless, uses external function "Mobility"}

d1, {diameter of small neutral particle : nm}

d2, {diameter of large charged or neutral particle : nm}

h, {extra distance : nm, typically 0.115}

gcm3, {small particle density : g cm^-3, typically 1.5-2}

q, {large particle charge : e}

aa, {small particle polarizability : angstrom^3}

d0, {critical diameter of quantum rebound : nm, typical 2.5}

T0, {extra temperature of quantum rebound: K, typically 300}

T, {air temperature : K}

mb, {air pressure : mb}

yua, {first dipole enhancement coefficient}

yub {second dipole enhancement coefficient} : double) : double;

{Two alternative methods can be used (dont use both simultaneously!):

1. In case of the method of effective polarizability the actual value of aa shold be presented and yua = yub = 0.

Polarizability aa in angstrom^3 is often estimated as equal to the number of atoms in a cluster or as equal to r^3 for large particles.

Polarizability of a molecule of sulphuric acid is extra high:

about 149 angstrom^3.

2. In case of the method by Nadykto and Yu the parameter aa must be zero, yua = sqr(f1 - 1) / (f2 - 1) and yub = ln((f1 - 1) / (f2 - 1)),

where f1 is Nadykto-Yu dipole enhanchement factor for d = 1 nm and f2 is Nadykto-Yu dipole enhanchement factor for d = 2 nm.

Nadykto and Yu expected f1 = 4.35 and f2 = 1.8 for sulphuric acid at temperature 298 K, in this case yua = 14 and yub = 1.43}

{Growth rate factor GR/GRo for the second substance, designed

as modification of function coag according to nano-Koehler model

GRo is plain Knudsen growth rate explained in (Tammet, Kulmala, 2005)}

function growthfactor2 ({dimensionless, uses external function "Mobility"} d1, {diameter of small neutral particle : nm}

d2, {diameter of large charged or neutral particle : nm}

h, {extra distance : nm, typically 0.115}

gcm3, {small particle density : g cm^-3} q, {large particle charge : e}

aa, {small particle polarizability : angstrom^3}

d0, {critical diameter of nano-Köhler model : nm, about3}

p, {power of the nano-Koehler model, about 2}

T, {air temperature : K}

mb {air pressure : mb} : double) : double;

{Polarizability aa in angstrom^3 is often estimated as equal to the number of atoms in a cluster or as equal to r^3 for larger particles.

NB: the second substance is usually an organic compound and has lower polarizability when compared with the sulphuric acid}

function

ion_needlesink

Z {ion mobility : cm² V^-1 s^-1},

dneedle {mm, about 0.9 for Pinus Sylvestris},

L {m^-2, total length of needles in 1 m^3 of canopy}, wind {m s^-1, inside of the canopy},

T {air temperature : K},

mb {air pressure : mb} : double) : double;

function

particle_needlesink

dparticle {nm},

gcm3 {particle density : g cm^-3},

dneedle {mm, about 0.9 for Pinus Sylvestris},

L {m^-2, total length of needles in 1 m^3 of canopy}, wind {m s^-1, inside of the canopy},

T {air temperature : K},

mb {air pressure : mb} : double) : double;

The The End End

Thank you for attention,

questions are welcome.