We now see that for a light molecule, with Mi much less than the ambient or mean atmospheric molecular weight M we have a strong buoyancy force for diffusion to space. When the molecular mixing ratio is constant, dfi/dz = 0, we are left with the buoyancy term that is commonly referred to as the limiting flux.

7.4 Surface deposition

The surface deposition loss rate term Sdi (molecules cm~3 s_1) depends on the atmospheric number density of the particles that are being deposited onto the surface. It can be written as where ni is the number density, and vi is the velocity of particle i measured positive in the downwards direction. Expanding the above derivative into its two components we can write dni dvi

If we are considering deposition onto a surface from an atmospheric layer just above the surface, then the deposition velocity at the surface boundary, z1 , is equal to the dry deposition velocity, vdi, while at the upper boundary, z2, of the layer it is zero. From eqn (7.28) we can approximately write for the loss rate at the lower boundary of the layer

H Z2 - zi where ni is the atmospheric number density of molecule i at the surface and H is the atmospheric number density scale height. We can derive a surface deposition flux Fdi (molecules cm~2 s_1) from the surface deposition velocity (cm/s) according to

Molecule |
T(° C) |
800 |
500 |
300 |
100 |
0 |

so2 |
0 |
980 |
980 |
980 |
990 |
1000 |

SO2 |
25 |
120 |
130 |
160 |
370 |
1000 |

O3 |
0 |
550 |
610 |
700 |
1000 |
3000 |

O3 |
25 |
100 |
110 |
130 |
320 |
950 |

NO2 |
0 |
3800 |
3800 |
3900 |
4300 |
9500 |

NO2 |
25 |
120 |
130 |
160 |
480 |
2800 |

H2O2 |
0 |
390 |
420 |
460 |
610 |
980 |

H2O2 |
25 |
80 |
90 |
110 |
250 |
640 |

N2O |
0 |
980 |
980 |
980 |
990 |
1000 |

N2O |
25 |
100 |
110 |
140 |
340 |
1000 |

NH3 |
0 |
1500 |
1500 |
1500 |
1500 |
1500 |

NH3 |
25 |
70 |
80 |
100 |
310 |
2600 |

and define a first-order, in n, loss rate (s at the surface from

Tldi

where Tdi is the mean lifetime of the molecule with respect to deposition.

7.4.2 Dry deposition velocities

The deposition velocity of gases is usually derived from a formula analogous to Ohm's law in electrical circuits

where Ra is the aerodynamic resistance determined by turbulence, Rb is referred to as the quasilaminar boundary layer resistance, often significantly smaller than Ra (typical values 50 s m-1), and Rc is the total surface resistance arising from uptake by vegetation, soil, water or ice. Considerable effort has been placed in evaluating Rc from

The vegetation resistance (stomatal resistance) is controlled by the solar flux (W m-2) incident on the vegetation and the surface air temperature. Thus, there is a feedback mechanism between molecules that control the radiation field and the indirect effect of radiation on atmospheric composition through vegetation uptake. In Table 7.2 are given typical values for the total surface resistance of a deciduous forest as a function of downwelling solar flux for various molecules.

In Table 7.3 are given the resistances to soil uptake and deposition onto water/ice surfaces. For large bodies of water, dry deposition (as opposed to removal by

Molecule |
Soil |
Water/ice |

so2 |
125 |
227 |

O3 |
400 |
2000 |

NO2 |
600 |
105 |

HNO3 |
10 |
10 |

NO2 |
600 |
105 |

NO |
105 |
105 |

CO |
2000 |
2.0x 104 |

H2 |
2650 |
3x 104 |

HCHO |
280 |
110 |

H2 O2 |
110 |
100 |

rain) of gases is primarily dependent on water solubility. Uptake of gases by soils is primarily dependent on biological activity in the soil, although other factors such as temperature, acidity and moisture are also important. Gases that react with the surface (O3, NO2), and gases that are highly soluble in water (HNO3, SO2, H2O2) are better sequestered by the surface, while inert gases (CO) have relatively low rates of surface deposition.

If we have a surface deposition rate Lid of a particular molecule i in Tg (1012 g) per year, then we can express this in terms of a mean deposition velocity and vice versa through

where n is the atmospheric number density (equal to the Loschmidt number 2.687x1019 cm-3 at STP), fi the mixing ratio of molecule i, NA = 6.0224 x 1023 is Avogadro's number, Mi is the molecular weight, and Ad is the total deposition surface area. As an example, for H2 with a mean global soil deposition rate of 56 Tg year-1, with global soil cover taken as 70% of global land surface area Ad = 0.70Ai, where the Earth's land surface area is Ai = 1.5 x 1018 cm2, n = 2.55 x 1019 molecules cm-3 (at 288 K), and fi = 530 ppbv we obtain a deposition velocity of 0.038 cm s-1 corresponding to a soil resistance of 2650 s m-1 or a soil deposition flux Fdi of 5.1 X1011 molecules cm-2 s-1. Globally, this corresponds to a mean surface flux of 1.06x 1011 molecules cm-2 s-1, a deposition velocity of 0.0078 cm s-1, which corresponds to a loss rate of 7.8x10-8 s-1 for a 1-km atmospheric layer.

Tropospheric gases that are highly soluble in water can be removed from the atmosphere through scavenging by rain drops. Their removal rate depends on cloud formation and rainfall. Gases like HNO3, HNO4, HCHO, CH3OOH and H2O2 have relatively short residence times against rainout of the order of 10 days,

Molecule |
Tg year 1 |
molecules cm 2 s 1 |

h2 |
51 |
9.72xl0lu |

ch4 |
600 |
1.44x 1011 |

CO |
2800 |
3.78x 1011 |

n2o |
25 |
2.17x109 |

co2 |
26 |
2.25x109 |

so2 |
150 |
8.93x 109 |

compared with say O2 with residence times of the order of 105 years. Thus, for these soluble gases a rainout rate of 10~6 is typical.

There are both natural and anthropogenic emission sources of molecules at the Earth's surface. Water vapour enters the atmosphere through evaporation from the oceans, evapotranspiration from plants and ejection from volcanoes. Carbon dioxide, methane, N2O, hydrogen, ammonia, for example, are produced by many natural processes related to biological cycles and also by industrial activities.

The surface emission term Si can be written in terms of the surface emission flux, Fei, dt J e dz

If we are considering emission from a surface into an atmospheric layer we can approximate the derivative of the flux in the layer by

where z2 is the upper boundary of the layer and z1 is the lower. For surface emission we can set flux1 = Fei, where Fei is the surface flux and flux2 = 0, hence the production rate within the layer is determined by the surface emission term

z2 - z1 surface flux

width of layer molecules emitted per second volume of layer

The atmospheric production rate is independent of the choice of the width of the layer, since for example doubling the layer width simply halves the production rate but production is distributed over twice as much of the atmosphere.

If we have a surface emission rate Lei of a particular molecule i in Tg (1012 g) per year, then we can express this as a surface flux, Fei of molecules cm~2 s_1 via p.- ^1Ql2jVA (7 48)

where Na is Avogadro's number, Mi is the molecular weight, and Ae is the total emitting surface area. In Table 7.4 are given estimates of total global emission rates for various gases.

Photolysis or photodissociation of a molecule is the dissociation of the molecule by radiation. Photodissociation is the process by which a molecule absorbs a photon of sufficient energy to overcome the bond holding the constituent atomic nuclei together. The bond arises from the shared electrons of the atoms that provide an electric field that overcomes the repulsive forces of the positively charged nuclei. Photoionization of a molecule or atom is the process by which a molecule or atom absorbs photons of sufficiently high energy to remove bound electrons and thus form positively charge ions.

The photolysis rate per second, j, at altitude z at time t is the inverse of the lifetime of a molecule before photolysis occurs, and is given by j (z,t)= f" fx(z,t)p0(t)SQXax (z)$x(z)d\, (7.49)

where SqX is the total solar irradiance or solar constant, fx is the enhancement factor, p0(t) is the cosine of the solar zenith angle. The absorption cross-section, ax can be temperature dependent as can be the quantum yield $x, which represents the probability that if a molecule absorbs a photon it will be photodis-sociated.

If there is no Earth-atmosphere reflectance of radiation to space at a particular wavelength, because for example the absorption is so strong, then there is only the downwards photon flux and so fx = 1 at the top of the atmosphere. If we have no atmospheric absorption or scattering but only surface reflection, by a surface with an albedo of 0.5, then fx = 1.5 at all altitudes. Finally, if we include multiple scattering between this reflecting surface and the atmosphere above, then the enhancement factor can rise above 2.0. Thus, multiple scattering and surface reflection can enhance the photolysis rate of an atmospheric molecule, while absorption of solar radiation by other molecules reduces the enhancement factor. We note that the maximum value for the enhancement factor at the top

Wavelength (nm)

Wavelength (nm)

Flg. 7.2. The photolysis enhancement factor fx at the top of the atmosphere for global mean Earth conditions.

of the atmosphere is 3.0 (§6.7). This arises because we are summing photons from all directions, both diffuse and direct as shown by eqn (6.135), that are incident on an element of volume containing the molecule.

In Fig. 7.2 is shown the enhancement factor fx at the top of the atmosphere for solar ultraviolet-visible radiation. The enhancement factor was calculated for global mean conditions with a solar zenith angle x, given by j = cos(x) = 0.5 and a planetary albedo of 0.33, based on a radiative-convective 1D model (Var-davas and Carver 1984) that includes cloud and Rayleigh scattering, molecular absorption, and a mean surface albedo of 0.1.

7.6.2 Quantum yield

The quantum yield is defined in various ways depending on its use. Some of the definitions are listed below:

number of molecules reacting per second number of quanta absorbed per second or number of product molecules

number of quanta absorbed

If the quantum yield is less than one it indicates that de-excitation of the molecule occurs by other processes (e.g. collisions) before photolysis takes place. If the quantum yield is greater than one it indicates a chain reaction.

Depending on the photon wavelength, a molecule can dissociate into different products. In this case we can add the various photolysis rates, corresponding to different spectral regions, to obtain the total photolysis rate. If the molecule can dissociate to different products for the same spectral interval, then we can define a probability for each possible outcome of products, or branching ratio, so that the sum of the branching ratios is unity.

In Appendix B (Tables B.2 and B.3) are given the spectral intervals of significant photolysis for various molecules, together with the total photolysis rate, and photolysis products and rates for the photolysis channels. Also given are the ionization rates for the main constituents of the upper atmosphere, and ionization products (Table B.1).

Absorption of visible and ultraviolet radiation by molecules occurs via transitions between vibrational-rotational sublevels of electronic states. Idealized potential-energy curves for some of the electronic states of O2 are shown in Fig. 7.3. Photodissociation of O2 can occur via transitions from the electronic ground state Xto the excited states A3£+ and B3£-. The notation is similar to electronic states of atoms with S, P, D, •• -, replaced by E, n, A, ••• (see Herzberg 1950). Photodissociation can occur via transitions from a bound level to the continuous region of an excited electronic state. The dissociation limit is then exceeded and the molecule breaks up. Photodissociation can also occur from bound-bound electronic transitions if there is a repulsive electronic state (dissociation continuum) that interacts with the vibrational-rotational energy levels of the upper electronic state of the transition. This is referred to as predissociation and it involves a nonradiative transition from the vibrational-rotational levels of the upper bound electronic state to the dissociation continuum of the repulsive state. The probability of predissociation increases if the potential energy of the vibrational-rotational level of the upper electronic state of the transition is higher than the crossing point of the potential curves of the repulsive and upper electronic states of the transition. Transitions from Xto the dissociation continuum of the state A3S+ (the forbidden Herzberg system) result in the dissociation of molecular oxygen via the channel

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