EPS 200 - Atmospheric Chemistry & Physics
What is a hectoPascal?
A hectoPascal (hPa) is equivalent to a millibar (mb), where 1mb = 100Pa. The atmospheric pressure at ground level is therefore 1013 mbar, 1013 hPa, or 1.013 bar.
What is the time scale for vertical transport from the surface to the tropopause?
About 3 months, faster vertical transport can take place by locally driven buoyancy.
What effect does solar UV radiation have on the temperature of the Earth?
Absorption of solar UV radiation by the ozone layer in the stratosphere generates a temperature inversion. Because of this inversion, vertical motions in the stratosphere are strongly suppressed (the stratosphere is stratified, hence its name). The temperature inversion also provides a cap for unstable motions initiated in the troposphere, and more generally suppresses the exchange of air between the troposphere and the stratosphere. This restriction of stratosphere-troposphere exchange limits the potential of many pollutants emitted at the surface to affect the stratospheric ozone layer.
What are typical sizes of aerosols in the atmosphere?
Aerosols are typically between 0.01 and 10 microns in diameter (smaller particles grow rapidly by condensation while larger particles fall out rapidly under their own weight). These are usually described by number concentration (number density) and mass concentration (mass of particles per unit volume of air).
What is the hydrosphere?
All of the oceans, lakes, rivers, and groundwater on the Earth.
What is the biosphere?
All the vegetation, animals, etc. on the Earth.
What are the four processes that control the concentrations of chemical species in the atmosphere?
- Emissions - anthropogenic, biogenic or non-biogenic sources - Chemistry - reactions in the atmosphere lead to formation and removal of species. - transport - winds transport atmospheric species away from their point of origin - deposition - all material in the atmosphere is eventually deposited back to the Earth's surface. Escape to outer space is negligible due to the Earth's gravitational pull. Dry deposition and wet deposition are possible.
What are the three measures of atmospheric composition?
- Mixing ratio - Number density - Partial pressure Each of these measures has its own application.
What is a torr?
1 torr = 1mm HG = 134 Pa
What is the mean lapse rate observed in the troposphere?
6.5K/km, corresponding to moderately stable conditions. A major reason for this stabiliy is the release of latent heat by cloud formation. Another reason is the vertical gradient of radiative cooling in the atmosphere.
How does cloud formation aid in atmospheric stability?
Although cloud formation increases buoyancy by providing latent heat release, it increases the stability of the surrounding atmosphere by providing a source of heat at high altitude.
How are the Westerlies created?
As the air from the Hadley cell subsides in the subtropical anticyclones it experiences a clockwise rotation in the northern hemisphere. Further poleward transport is difficult because of the strong Coriolis force, which tends to produce a geostrophic longitudinal flow (the westerlies) by balancing the meridional pressure-gradient force. For air to move poleward it must lose angular momentum; this loss is accomplished by friction at the surface, and is more efficient in the northern hemisphere, where large land masses and mountains provide roughness. This difference between the two hemispheres explains the more persistent westerlies in the southern midlatitudes, and the particularly cold antarctic atmosphere.
Explain physically what occurs when an air parcel rises in the atmosphere due to buoyancy effects.
Assume that by some external force the air parcel A is pushed upward from z to z+dz and then released. The pressure at z+dz is less than that at z. Thus the air parcel expands, and in doing so performs work (dW=-PdV). Let us assume the air parcel does not exchange energy with its surroundings as it rises (i.e. adiabatic dQ = 0). The work is then performed at the expense of internal energy E of the air parcel: dE = dW + dQ = -PdV < 0. Since the internal energy of an ideal gas is a function of temperature only (Joule's second law), the air parcel cools. The air parcel cools during ascent but does not become heavier than its surroundings and sink back to its original position. The temperature of the surrounding atmosphere also usually decreases with altitude. Whether the parcel keeps rising depends on how rapid its adiabatic cooling rate is relative to the change of temperature with altitude in the surrounding atmosphere.
At what height does the atmospheric pressure reduce to 0.01 hPa (0.001% of total atmospheric pressure)?
At 80km altitude, this means that at this point we are on the brink of space, since 99.999% of the atmosphere is contained below this altitude. From this we can see that the atmosphere is relatively think compared to the Earth itself.
Why are there many deserts at around 30 degree latitude?
At about 30 degrees north and south are regions of prevailing high pressure, with centers of high pressure (subtropical anticyclones) generally over the oceans. High pressure is associated with dry conditions, and indeed one finds that the major deserts of the world are at about 30 degrees latitude.
What are the 'roaring forties' and 'screaming fifties'?
At higher latitudes (mid-latitudes) the winds shift to a prevailing westerly direction (westerlies). These winds are considerably more consistent in the southern hemisphere than in the northern hemisphere.
Why is there a significant kinetic barrier to ice formation in the atmosphere?
Because of the paucity of aerosol surfaces that may serve as templates for condensation of ice crystals. As a result, cloud liquid water readily supercools (remains liquid) down to temperatures of about 250K.
What are the two simplest types of models used in atmospheric chemistry?
Box models and puff models. These two models represent respectively the simplest applications of the Eulerian and Lagrangian approaches to obtain approximate solutions of the continuity equation.
How does buoyancy affect the atmosphere?
Buoyancy in the atmosphere is determined by the vertical gradient of temperature. This is the cause of the popular phrase 'warm air rises'. Actually this statement is incorrect; warm air does not inherently rise, it rises because its surroundings are relatively cool, which induces an acceleration due to buoyancy.
How is cloud formation controlled by saturation pressure?
Cloud formation in the atmosphere takes place when P_H2O >= P_H2O,sat and it is therefore important to understand how P_H2O,sat depends on environmental variables. From the phase rule, the number n of independent variables determining the equilibrium of c chemical components between a number p of different phases is given by: n = c+2-p In the case of equilibrium of liquid water with its vapor there is only one component and two phases. Thus the equilibrium is determined by one single independent variable; at a given temperature there is only one saturation vapor pressure for which liquid and gas are in equilibrium.
At what specific value of relative humidity does cloud formation occur?
Cloud formation takes place when RH >= 100%
What is latent heat release with respect to cloud formation?
Cloudy conditions represent an exception to the constancy of the adiabatic lapse rate. Condensation of water vapor is an exothermic process, meaning that it releases heat (aka latent heat release). Cloud formation in a rising air parcel provides an internal source of heat that partly compensates for the cooling due to expansion of the air parcel and therefore increases its buoyancy. Therefore, air parcels rise adiabatically up to the cloud layer, with an adiabatic lapse rate of 9.8K/km. At the layer where clouds form, 100% RH is reached and cloud forms. Above this layer, cloud air parcels continue to rise; condensation of water vapor releases heat and the lapse rate decreases and varies from 2-7K/km. We refer to buoyant motions in cloud as wet convection. The lapse rate of a cloudy air parcel is called the wet adiabatic lapse rate gamma_w and ranges from 2-7K/km depending on the water condensation rate. An atmosphere with rate gamma_w < -dT/dz < gamma is called conditionally unstable.
When might one use partial pressures as the way of describing atmospheric composition?
Concentrations of water vapor and other gases that are of most interest because of their phase changes are often given as partial pressures. The partial pressure of a gas measures the frequency of collisions of gas molecules with surfaces and therefore determines the exchange rate of molecules between the gas phase and a coexistent condensed phase.
What are the major sources of heat in the atmosphere?
Condensation of water vapor, and the absorption of UV radiation by ozone.
Derive the adiabatic lapse rate.
Consider a thermodynamic cycle consisting of an adiabatic expansion, followed by an isothermal compression and then isobaric heating. The cycle returns the air parcel to its initial thermodynamic state and must therefore have zero net effect on any thermodynamic function. Considering enthalpy: H = E + PV -> dH=dE+d(PV) = dW+dQ+d(PV) where dW=-PdV is the work performed on the system and dQ is the heat added to the system. dH=-PdV +dQ+PdV+VdP=dQ+VdP For the adiabatic process, dQ=0 by definition so that dH_1 = VdP For the isothermal process (II), dE=0 (internal energy of an ideal gas is a function of temperature only) and d(PV)=0 (ideal gas law), hence: dH_2 = 0 For the isobaric process (III) we have: dH_3=dQ=m*C_p*(T(z)-T(z+dz))=-m*C_p*dT dH_1+dH_2+dH_3 = 0 VdP = m*C_p*dT Noting that m=p*V we can define the adiabatic lapse rate (dT/dz = gamma) as: gamma = - dT/dz = g/C_p = 9.8 K/km gamma is a constant independent of atmospheric conditions. We can diagnose whether an atmosphere is stable or unstable wrt to vertical motions simply by comparing its lapse rate to gamma = 9.8 K/km dT_atm/dz > gamm --> unstable dT_atm/dz = gamma --> neutral dT_atm/dz < gamma --> stable Particularly stable conditions are encountered when the temperature increases with altitude (dT_atm/dz > 0 ) like in the stratosphere, such a situation is called a temperature inversion.
Describe the mechanism of geostrophic flow.
Consider an air parcel initially at rest in a pressure-gradient field in the northern hemisphere. There is no Coriolis force applied to the air parcel since it is at rest. Under the effect of the pressure-gradient from high to low pressure, i.e. perpendicularly to the isobars (lines of constant pressure). As the air parcel acquires speed, the increasing Coriolis acceleration causes it to curve to the right. Eventually, an equilibrium is reached when the Coriolis force balances the pressure-gradient force, resulting in a steady flow (zero acceleration). This steady flow is called the geostrophic flow.
What is subsidence inversion and how is it related to the PBL?
Consider an air parcel rising from the surface in an unstable atmosphere. This air parcel cools following the dry adiabatic lapse rate up to a certain altitude z_c at which the saturation point of water is reached and clouds form. As the air parcel rises further it cools following a wet adiabatic lapse rate; for simplicity assume that this rate is constant with altitude, although it would be expected to vary as the condensation rate of water changes. Eventually, precipitation forms, removing the condensed water from the air parcel. Ultimately, the air parcel reaches an altitude z_t where it is stable wrt the surrounding atmosphere. This altitude defines the top of the cloud. As the air parcel flows out of the cloud at altitude z_t, it has lost most of its water to precipitation. The outflowing air is then carried by the winds at high altitude and must eventually subside for mass conservation of air to be satisfied. As the air subsides, its temperature increases following the dry adiabatic lapse rate. Assume that the subsidence takes place over a region B that has the same surface temperature T_o as region A. For any given altitude over region B, the air subsiding from z_t is warmer than the air rising from the surface; this situation leads to stable conditions; often manifested by a subsidence inversion (typically 1-3km altitude) where the subsiding air meets the air convecting from the surface. The stability induced by subsidence is a strong barrier to buoyant motion over region B. Vertical mixing of surface air above region B is limited to the atmospheric column below the subsidence inversion; this column is commonly called the planetary boundary layer. Strong and persistent subsidence inversions can lead to accumulation of pollutants in the PBL over several days, resulting in air pollution episodes. This is especially an issue in large subtropical cities of the world (e.g. LA, Mexico City, Athens, and Sao Paulo).
Is the atmosphere generally turbulent or laminar?
Consider the Reynolds number, a characteristic value that can be used to determine the transition from laminar to turbulent flows. Re = U*L/v In the atmosphere, U and L are large values, since the speeds are fast and the length scales large, this means that typically Reynolds numbers are above 10000 and are hence turbulent in nature. This turbulence is evident when one observes the dispersion of a combustion plume emanating from a cigarette, barbecue, or a smokestack.
What is the atmospheric column of a gas X?
Consider the atmosphere extending from the Earth's surface to a certain to p (z_T) above which number densities are assumed negligibly small. A slab of uniform horizontal surface area and vertical thickness dz contains n_x*dz molecules of X. The integral over the depth of the atmosphere defines the atmospheric column of X.
What is the most severe gas in the atmosphere that contributes to the greenhouse effect?
Contrary to popular belief, water vapor is actually the most severe contributor to the greenhouse effect. However, the effect of this has been relatively constant since pre-industrial times, so it is not considered to be a contributor to global warming.
What is Dalton's law?
Dalton's law states that the partial pressure, P_x, is related to the total pressure by the mixing ratio (or mole fraction): P_x = C_x * P , where P is the total atmospheric pressure. Therefore we can use the ideal gas law to relate P_x to n_x: P_x = n_x * R * T / A_v
What is the difference between dry and wet deposition?
Dry deposition involves direction reaction or absorption at the Earth's surface, such as uptake of CO(2) by photosynthesis. Wet deposition involving scavenging by precipitation.
How can one calculate the number density of air and CO(2) at sea level under STP?
First determine the number density of air by considering the ideal gas law: PV = nRT -> P/RT = n/V = n_a / A_v n_a = A_v * P/ (R*T) Then use the mixing ratio of CO(2) and multiply by the number density of air: n_CO2 = C_CO2 * n_a
Describe some features of the barometric law.
For a mean atmospheric temperature of 250K, the scale height H = 7.4km. The barometric law explains the observed exponential dependence of P on z, and a plot of z vs ln P yields a straight line with slope -H. This equation can also be rewritten in terms of the air density if one assumes T is constant: p_a(z) = p_a(0)exp(-z/H) One can also write a similar equation for the air number density. For every H rise in altitude, the pressure and density of air drop by a factor of e = 2.7; thus H provides a convenient measure of the thickness of the atmosphere.
What is the importance of geochemical cycles of the concentration of species in the atmosphere?
From an Earth system perspective, the composition of the atmosphere is ultimately controlled by the exchange of elements between the different reservoirs of the Earth, in so called biogeochemical and geochemical cycles that regulate the atmospheric abundance of N(2), O(2), and CO(2).
What are trace gases?
Gases other than N(2), O(2), argon and water exist in the atmosphere, but at extremely low concentrations. These are known as trace gases. These can still be of critical importance for the greenhouse effect, the ozone layer, smog, and other environmental issues.
What is meant by the term geochemical cycling?
Geochemical cycling refers to the flow of elements through the Earth's reservoirs; the term underlines the cyclical nature of the flow in a closed system.
How is geostrophic flow formed in the atmosphere?
Geostrophic flow is the result of a balance between the pressure-gradient force and the Coriolis force in the atmosphere, when considering horizontal directions (across latitude and longitude). Below 1km altitude, the horizontal flow is modified by friction from the PBL. Geostrophic flow is driven by horizontal pressure gradients created by differential heating of the Earth's surface.
What is the Hadley circulation?
Hadley envisioned the circulation as a global sea breeze driven by the temperature contrast between the hot equator and the cold poles. This model explains the presence of the ITCZ near the equation and the seasonal variations in the location of the ITCZ (as the region of maximum heating follows the Sun from the southern tropics in January to the northern tropics in July). A flaw is that it does not account for the Coriolis force. Air in the high altitude branches of the Hadley circulation cells blowing from the equator to the pole is accelerated by the Coriolis force as it moves poleward eventually breaking down into an unstable flow. Consequently, the Hadley cells extend only from the equator to about 30 degrees latitude. At 30 degrees the air is pushed down, producing the observed subtropical high-pressure belts. The Hadley cells remain a good model for the circulation of the tropical atompshere.
How does diurnal cycling of temperature affect the lower atmosphere?
Heating and cooling of the surface affects the stability of the atmosphere. The Earth's surface is much more efficient at absorbing and emitting radiation than the atmosphere. During daytime, heating of the surface increases air temperatures close to the surface, resulting in an unstable atmosphere. In this unstable atmosphere the air moves freely up and down, following the adiabatic lapse rate, so that the atmospheric lapse rate continually adjusts to gamma; unstable lapse rates are almost never actually observed in the atmosphere except in the lowest few meters above the surface. The observation of an adiabatic lapse rate is in fact a sure indication of an unstable atmosphere. At sunset the land surface cools, setting up stable conditions near the surface. Upward transport of the cold surface air is then hindered by the stable conditions. If winds are low, a temperature inversion typically develops near the surface. If winds are strong, the cold surface air is forced upward by mechanical turbulence and moderately stable conditions extend to some depth in the atmosphere. After sunrise, heating of the surface gradually erodes the stable atmosphere from below until the unstable daytime profile is reestablished. We cal the unstable layer in direct contact with the surface the mixed layer, and the top of the mixed layer is the mixing depth; the mixing depth z_i for the morning profile in Figure 4-18. The mixing depth does not usually extend to more than about 3km altitude, even in the afternoon, because of capping by subsidence inversions. This diurnal variation in atmospheric stability over land surfaces has important implications for urban air pollution; ventilation of cities tend to be suppressed at night and facilitated in the daytime. In winter when solar heating is weak, breaking of the inversion is difficult and accumulation of pollutants may result in severe air pollution episodes.
What are the dimensions of the sea-breeze circulation?
Horizontally the sea-breeze circulation extends 10km, and vertically it is approximately 1km. At night a reverse circulation is frequently observed (the land breeze) as the land cools faster than the sea.
What is a convective atmosphere?
If an air parcel at a specific height has a temperature greater than its surroudings, it will accelerate upwards by buoyancy. The atmosphere is unstable wrt vertical motion, because any initial push upward or downward on the air parcel will be amplified by buoyancy. We call such an atmosphere convective and refer to the rapid buoyant motions as convection. On the contrary, if the temperature of the parcel is less than the surroundings, the rising air parcel is colder and heavier than the surroundings and sinks back to its position of origin; vertical motion is suppressed and the atmosphere is stable.
What are meant by the terms 'inventory' and 'reservoir' in terms of a box model?
In a one-box model for an atmospheric species X, the mass of X in the box is often called an inventory and the box itself is often called a reservoir.
What are aerosols?
In addition to gases in the atmosphere, it also contains solid or liquid particles suspended in the gaseous medium, these are known as aerosols. An aerosol is a general term describing a dispersed condensed phase suspended as a gas.
Why can we use the ideal gas law in atmospheric chemistry?
Pressures in the atmosphere are sufficiently low that the ideal gas law is always obeyed to within 1%.
What are some interesting features of the turbulent diffusion parameterization term, K_z?
In practice, one finds that K_z does not depend much on the nature of the diffusing species and can be expressed with some reliability in the lower troposphere as a function of (a) the wind speed and surface roughness (which determine the mechanical turbulence arising from the collision of the flow with obstacles), (b) the heating of the surface (which determines the buoyant turbulence), and (c) the altitude (which determines the size of the turbulent eddies). Order of magnitude values for K_z are 10^2 - 10^5 cm^2 s^-1 in a stable atmosphere, 10^4 - 10^6 in a near-neutral atmosphere, and 10^5 - 10^7 in an unstable atmosphere.
During the debate over the harmful effects of CFCs on stratospheric ozone, some scientists claimed CFCs could not possibly reach the stratosphere because of their high molecular weights and hence low scale heights, why is this incorrect?
In reality, turbulent mixing of air ensures that CFC mixing ratios in air entering the stratosphere are essentially the same as those in surface air. This is because gravitational separation of the air mixture takes place by molecular diffusion, which is considerably slower than turbulent vertical mixing of air for altitudes below 100km. Only above 100km does significant gravitational separation of gases begin to take place.
How does geostrophic flow influence movements in the Northern and southern hemisphere, in terms of cyclones and anticyclones?
In the Northern hemisphere, the geostrophic flow is such that the higher pressure is to the right of the flow; air flows clockwise around a center of high pressure and counterclockwise around a center of low pressure. The direction of flow is reversed in the southern hemisphere. A center of high pressure is called an anticyclone or a simply a high. A center of low pressure is called a cyclone or simply a low.
What are some discerning features of the mesosphere?
In the mesosphere, above the ozone layer, the temperature decreases with altitude. The mesosphere extends up to 80km (mesopause) above which lies the thermosphere where temperature increases again with altitude due to absorption of strong UV solar radiation by N(2) and O(2).
How can we parameterize turbulence in the smokestack example?
In this time-averaged, smoothed plume there is a well-defined plume centerline, and a decrease of pollutant mixing ratios on both sides of this centerline that can be approximated as Gaussian. We draw a parallel to the Gaussian spreading in molecular diffusion, which is a consequence of the linear relationship between the diffusion flux and the gradient of the species mixing ratio (Fick's law): F = -n_a * D * dC/dz F is the molecular diffusion flux, D is the molecular diffusion coefficient. Fick's law is the postulate on which the theory of molecular diffusion is built. Molecular diffusion is far too slow to contribute significantly to atmospheric transport, but the dispersion process resulting from turbulent air motions resembles that from molecular diffusion. We define by analogy an empirical turbulent diffusion coefficient K_z as: Fbar = -n_a*K_z* dCbar/dz where Fbar is the turbulent flux and Cbar is the time-averaged mixing ratio. This equation defines the turbulent diffusion parameterization of turbulence. K_z is an empirical quantity and must therefore be determine experimentally by concurrent measurements of Fbar and dCbar/dz.
Why is the turbulent diffusion parameterization of turbulence useful?
It can be used to estimate time scales for vertical transport in the troposphere. We wish to know the mean time dt required by an air molecule to travel a vertical distance dz. Einstein's equation for molecular diffusion (derived from Fick's law) gives dt = (dx^2)/2D where dx = distance travelled in any direction over time dt (molecular diffusion is isotropic). We can apply this to vertical turbulent motions in the atmosphere, replacing dx with dz and D by K_z: dt = (dz^2)/K_z A mean value for K_z in the troposphere is about 2x10^5 cm^2 s^-1. Inserting this into the above formula, we find that it takes on average about one month for air to mix vertically from the surface to the tropopause (dz ~ 10km); species with lifetimes longer than a month tend to be well mixed vertically in the troposphere, while species with shorter lifetimes show larger vertical gradients. Mixing within the PBL takes 1-2days, while ventilation of the PBL with air from the middle troposphere takes on average about a week. Vertical mixing of the unstable mixed layer produced by solar heating of the surface requires less than one hour. Exchange of air between the troposphere and stratosphere is considerably slower than mixing of the troposphere because of the temperature inversion in the stratosphere. It takes 5-10 years for air from the troposphere to be transported up to the stratosphere, and 1-2 years for air from the stratosphere to be transported down to the troposphere. This upward transport principally occurs in the tropics, and is returned from the stratosphere to the troposphere at midlatitudes, but the mechanisms are still not well understood.
What are the typical time scales for global transport in the troposphere?
Longitudinal wind speeds are of the order of 10 m/s , and observations show it takes only a few weeks for air to circumnavigate the globe in a given latitudinal band. Meridional transport is slower; winds speeds are of the order of 1 m/s, and it takes typically 1-2 months for air at midlatitudes to exchange with the tropics or polar regions. Interhemispheric transport is even slower because of the lack of thermal forcing across the Equator. It thus takes about 1 year for air to exchange between the northern and southern hemispheres.
Mass within the Earth's biosphere, atmosphere, lithosphere, and hydrosphere is relatively constant. However, a small amount of this mass is removed and gained, by what mechanisms can this occur?
Mass can be transferred to the deep Earth (such as the mantle or core) via the process of subduction of tectonic plates, and released by volcanism. Both these processes are very slow compared to the cycling elements between the surface reservoirs. They can also be released into space by the chemicals escaping (typically light elements) and produced by meteorites striking the Earth. All these processes are very slow compared to geochemical cycling.
What is an important application of number densities?
Measuring the absorption or scattering of a light beam by an optically active gas depends on the number of molecules of gas along the path of the beam and therefore on the number density of the gas.
What is the difference between aeronomy and meteorology?
Meteorology is associated with the study of the lower atmosphere, namely the troposphere and the stratosphere, whereas aeronomy is associated with the upper levels of the atmosphere such as the mesosphere and thermosphere.
Why is mixing ratio a useful way of describing atmospheric composition?
Mixing ratio of a gas remains constant when the air density changes (as happens when the temperature or the pressure changes). This can be understood by considering a balloon rising and expanding.
What is the mixing ratio?
Mixing ratio, C_X of a gas X (also called the mole fraction) is defined as the number of moles of X per mole of air. It is given in units of mol/mol (volume of gas per volume of air).
What is the molar composition of the atmosphere?
N(2) has a mixing ratio of 0.78 (i.e. 78% of all molecules in the atmosphere are nitrogen). O(2) has a ratio of 0.21, then argon with 0.0093 mol/mol. Water vapor ratios vary from 10^-6 to 10^-2. This variability is due to differing humidity in the atmosphere, which affects the ability to evaporate sweat and dry clothes on a washing line.
What are the trade winds?
North and south of the ITCZ and extending to about 20-30 degrees latitude, is the tropical regime of easterly 'trade winds', as blowing from East to West.
What is number density?
Number density of a gas X is defined as the number of molecules of X per unit volume of air. It is commonly expressed in units of molecules cm^-3 (number of molecules of X per cm^-3 of air). Number densities are important for calculating gas-phase reaction rates.
Compare the speeds of vertical and horizontal transport in terms of turbulent flux of a smokestack.
One can apply the same distinction between mean advective flux and turbulent flux to horizontal motions. Mean winds in the horizontal direction are ~1000 times faster than in the vertical direction, and are more organized, so that the advective flux usually dominates over the turbulent flux as long as dt is not too large (say less than a day). The distinction between mean advective flux and turbulent flux depends on the choice of dt; the larger dt, the greater the relative importance of the turbulent flux.
What are the main issues associated with a one-box model?
One-box models do not resolve the spatial distribution of the concentration of X inside the box. It is frequently assumed that the box is well-mixed in order to facilitate computation of sources and sinks.
What is the typical concentration of ozone in the atmosphere?
Ozone concentrations are typically described in parts per billion, and a normal concentration in the atmosphere would be 10-70 ppb. It is commonly known that an increase in ozone concentration of 10ppb can increase risk of respiratory death by 4%.
How does pressure vary through the atmosphere?
Pressure decreases exponentially with altitude.
How is relative humidity defined?
RH(%) = 100* P_H2O / P_H2O,sat (T) Weather reports typically describe water vapor concentrations in terms of relative humidity or dew point (T_d).
How can the exponential dependency of pressure on atmospheric height be derived from the barometric law?
Starting from the barometric law and substituting the ideal gas equation, we obtain the differential equation: dP/P = - (M_a*g)/(R*T) * dz By assuming that T is constant with altitude (T varies by only 20% below 80km) we obtain: ln(P(z)) - ln(P(0)) = - (M_a*g)/(R*T) * z After combining the logarithms and then taking the exponential, this is rewritten as: P(z)=P(0)exp(-M_a*g*z/R*T), this is specifically known as the barometric law. It can be simplified by defining a scale height H for the atmosphere: H=R*T/M_a*g, giving us P(z)=P(0)exp(-z/H)
What are the cruising altitudes of subsonic and supersonic aircraft and what is the difference in air density between these two altitudes?
Subsonic - 12km altitude Supersonic - 20km altitude Apply the barometric law in density form and use z = 12km and 20km, with H=7.4km (for air), then we obtain p(z_2)/p(z_1) = exp(-z_2/H)/exp(-z_1/H) = exp(-(z_2-z_1)/H) = 0.34 Therefore the air density at 20km is a third of that at 12km. The high speed of supersonic aircraft is made possible by the reduced air resistance at 20km.
What is the formula for the Coriolis acceleration applied to horizontal motions?
The Coriolis force acts on any object moving towards or away from a rotational frame of reference, and applies a force to it such that angular momentum is conserved (i.e. speeds up if object moves towards center of reference and slows down if object moves away). This force deflects objects in the Northern hemisphere to the right, and in the southern hemisphere to the left. Coriolis acceleration = 2*omega*v*sin(lambda) where omega is the angular velocity of the Earth and v is the speed of the moving object in the rotating frame of reference. The Coriolis force is zero at the equator and increases with latitude. The Coriolis force is always zero for an object at rest in the rotating frame of reference (v=0)
What is the lithosphere?
The Earth's crust
Consider a black parking lot where the surface temperature is 301K and is slightly warmer than the surrounding area of 300K. What is the buyoant acceleration of the air over the parking lot?
The acceleration due to buoyancy can be related to Archimedes law where in terms of density perturbations, by recalling that p ~ 1/T from the ideal gas law, we can obtain this in terms of temperature: y_b = (p'-p)/p * g = (1/T' - 1/T)/(1/T) * g = (T' - T)/T * g = 3.3x10^-2 m/s^2 This means that a difference of 1K can induce a vertical velocity of 3.3 cm/s in one second. Compare this to the vertical velocities of the order of 0.1 cm/s derived from general circulation. Such a large acceleration arising from only a modest temperature difference illustrates the importance of buoyancy in determining vertical transport in the atmosphere.
What is meant by the term atmospheric pressure?
The atmospheric pressure is the weight exerted by the overhead atmosphere on a unit area of surface. It can be measured with a mercury barometer, consisting of a long glass tube full of mercury inverted over a pool of mercury.
What is the barometric law?
The barometric law is the same as the hydrostatic law, it can be derived by considering an energy balance due to considerations of buoyancy, the equation describing the barometric law is: dP/dz = -p_a * g , where p_a is the atmospheric density and can be substituted for the ideal gas law: p_a = P*M_a / (R*T)
What is the dew point temperature?
The dew point is defined as the temperature at which the air parcel would be saturated with respect to liquid water: P_H2O = P_H2O,sat(T_d) At temperatures below freezing, one may also report the frost point T_f corresponding to saturation with respect to ice.
What is the ITCZ?
The intertropical convergence zone (ITCZ) is identifies a ribbon of atmosphere near the equator, only a few hundred km wide, with persistent convergence and associated clouds and rain. The clouds often extend up to the tropopause. The location of the ITCZ varies slightly with season, moving north from January to July.
What is the lifetime of a species X in a one-box model?
The lifetime T of X in the box is defined as the average time that a molecule of X remains in the box, that is, the ratio of the mass m of X in the box compared to the removal rate (F_out + L + D): T = m / (F_out + L + D) We can think of these in terms of separate lifetimes related to the removal of X by flow (T_F,out), removal by chemical reactions (T_L) and removal by deposition (T_D), giving: 1/T = 1/T_F,out + 1/T_L + 1/T_D
What is an interchangeable term for the lifetime of a species in the atmosphere?
The lifetime is also often called the residence time. One tends to refer to lifetime when the loss is by a chemical process such as L, and the residence time when the loss is by a physical process such as F_out or D.
How can the loss rate of a reactant in a bimolecular gas-phase reaction be determined?
The loss rate of X in a reaction: X+Y->P+Q, is equal to the frequency of collisions between molecules of X and Y, multiplied by the probability that a collision will result in a chemical reaction. Collision frequency is proportional to the product of number density n_x * n_y
What is the mass concentration of a gas X?
The mass concentration represents the mass of X per unit volume of air (denoted by p_x for the mass density of a body). This is closely related to the number density by: p_x = n_x * M_x / A_v
What is the mass of the atmosphere?
The mass of the atmosphere can be determined by considering Newton's second law, F=ma, where acceleration is due to gravity, g, and m is the mass of the Earth. The corresponding force is due to the atmospheric pressure multiplied by the surface area of the Earth, therefore: m_a = 4*PI*R^2 * P_S / g = 5.2x10^18 kg. The radius of the Earth is 6400km and the global mean pressure at the surface of the Earth is 984 hPa. The total number of moles of air in the atmosphere is N_a = m_a / M_a = 1.8x10^20 moles.
What is one of the major differences between the number density and the mixing ratio?
The mixing ratio (or mole fraction) does not changes as the density (and hence pressure and temperature) changes. However, the number density is a function of both pressure and temperature.
What is the molecular weight of moist air like you may find in tropical oceans when the mixing ratio of water can be as high as 0.03?
The molecular weight of M_a of moist air is given by: M_a = (1-C_H2O)*M_a,dry + C_H2O * M_H2O where M_a,dry = 28.96 x 10^-3 kg/mol is the molecular weight of dry air and M_H2O = 18*10^-3 kg/mol. For C_H2O = 0.03 we obtain M_a = 28.63x10^-3 kg/mol. The conclusion is that a mole of moist air is lighter than a mole of dry air.
How can we calculate the mean molecular weight of air?
The molecular weight of air can be calculated by summing up all of the components of the atmosphere as products of their respective mole fractions and molecular weights: M_a = SUM(C_i * M_i) M_a = C_N2 * M_N2 + C_O2 * M_O2 + C_Ar * M_Ar = 28.96 x 10^-3 kg/mol
What is a partial pressure of a gas X?
The partial pressure P_x of a gas X in a mixture of gases of total pressure P is defined as the pressure that would be exerted by the molecules of X if all the other gases were removed from the mixture.
What is the lapse rate and how is it related to atmospheric stability?
The rate of decrease of temperature with altitude (-dT/dz) is called the lapse rate. To determine whether an atmosphere is stable or unstable, we need to compare its atmospheric lapse rate (-dT_atm/dz) to the adiabatic lapse rate (-dT_a/dz). where T_a is the temperature of an arbitrary air parcel. Stability is a local property of the atmosphere defined by the local value of the atmospheric lapse rate; an atmosphere may be stable at some altitudes and unstable at others. Note that stability refers to both upward and downward movements. If an atmosphere is unstable wrt rising motions it is equivalently unstable wrt sinking motions. Instability thus causes rapid vertical mixing rather than unidirectional transport.
What is meant by a first-order sink in a box-model?
The sinks F_out, L, and D are often first-order, meaning that they are proportional to the mass inside the box (the more you have, the more you can lose). In that case, the lifetime is independent of the inventory of X in the box
What are some discerning features of the stratosphere?
The stratosphere extends from the top of the troposphere (the tropopause) to about 50 km altitude (the stratopause) and is characterized by an increase of temperature with altitude due to absorption of solar radiation by the ozone layer.
How much of the atmospheric mass is contained in the troposphere and the stratosphere?
The troposphere contains 90% of the total atmospheric mass, mostly due to the abundance of water vapor within this layer. The troposphere and stratosphere together account for 99.99% of the total atmospheric mass and are the domains of main interest from an environmental perspective. The mesosphere contains only about 0.1% of the total atmospheric mass.
What are some discerning features of the troposphere?
The troposphere extends from the surface to the tropopause at 8-18 km altitude depending on latitude and season. It is characterized by a decrease in temperature with altitude which can be explained simply (but not quite correctly) by solar heating of the surface.
What is the eddy correlation technique?
The use of collocated, high-frequency measurements of C and w to obtain the vertical flux of a species, is called the eddy correlation technique. It is so called because it involves determination of the covariance, or correlation, between the 'eddy' (fluctuating) components of C and w. Eddy correlation measurements from towers represent the standard approach for determining biosphere-atmosphere exchange fluxes of CO(2) and many other gases. Application of this technique is often limited by the difficulty of making high-quality measurements at such high frequencies (1Hz or better) to resolve the correlation between C' and w'
What is the relationship between the number density and mixing ratio?
These two quantities are related by the number density of air: n_x = C_x * n_a The number density of air is in turn related to the atmospheric pressure by the ideal gas law: PV = NRT n_a = A_v * N / V, where A_v is Avogadro's number, N is the moles of air and V is the volume. Therefore: n_a = A_v * P / (R*T) n_x = A_v * P * C_x / (R*T)
What is the importance of an atmospheric column of gas?
This atmospheric column determines the total efficiency with which the gas absorbs or scatters light passing through the atmosphere. For example, the efficiency with which the ozone layer prevents harmful UV radiation from reaching the Earth's surface is determined by ozone's atmospheric column.
How are species transported across from the northern to southern hemisphere?
This exchange takes place in part by horizontal mixing of convective storm outflows at the ITCZ, in part by season shift in the location of the ITCZ which causes tropical air to slosh between hemispheres, and in part by breaks in the ITCZ caused for example by land-ocean circulations such as the Indian monsoon.
What is the Coriolis force?
To an observer fixed in space watching the Earth rotate, an object fixed to the Earth at latitude lambda is traveling in a circle at a constant translational speed in the longitudinal direction: v_E = 2*PI*R*cos(lambda)/t where t = 1 day. For lambda = 42 degrees (Boston), we find v_E = 1250 km/hr. Note that v_E decreases with increasing latitude; it is this latitudinal gradient that causes the Coriolis force.
What is the objective of atmospheric chemistry?
To understand the factors that control the concentrations of chemical species in the atmosphere.
What are common mixing ratios for trace gases?
Typically, trace gases are described in parts per million volume (ppmv or ppm), parts per billion volume (ppbv or ppb), or parts per trillion volume (pptv or ppt). For example, present day CO(2) concentration is around 400 ppm (400x10^6 mol/mol).
How long on average does it take an air molecule to travel 1m by molecular diffusion? To travel 10m?
Using the adapted Einstein equation: dt = (dz^2)/K_z D = 0.2 cm^2 s^-1, we find that if dz = 1m, then dt = 6.9 hours. The time required to travel 10m is 690 hours or ~1month. Molecular diffusion is evidently unimportant as a means of atmospheric transport mixing at sea level. It becomes important only above 100km altitude.
When it is useful to use a quantity showing the fraction of mass removed by a single sink in a one-box model?
We are often interested in determining the relative importance of different sinks contributing to the overall removal of a species. For example, the fraction f removed by export out of the box is given by: f = F_out / (F_out + L + D)
If pre-industrial CO(2) levels were 280 ppmv and now they are 365 ppmv today, what is the corresponding increase of atmospheric carbon? Assume CO(2) is well mixed in the atmosphere.
We need to determine how the mixing ratio of CO(2) compares to the corresponding mass of carbon. C_CO2 = n_CO2 / n_a = N_C/N_a = M_a/M_C * m_c/m_a. We have now related the mixing ratio to the mass of carbon, now we must perturb the mass of carbon and mixing ratio to determine the increase in mass: D(m_c) = m_a * (M_c/M_a) * D(C_CO2) = 5.2x10^18 * (12x10^-3 / 29x10^-3) * (365x10^-6 - 280 x 10^-6) = 1.8 x 10^14 kg = 180 billion tons increase in carbon in the atmosphere!
What is the vertical turbulent flux of a smokestack discharging a pollutant X?
We wish to determine the vertical flux F of X at some point M downwind of the stack. The number of molecules of X crossing an horizontal surface area dA centered on M during time dt is equal to the number n_x*w*dt*dA of molecules in the volume element, where w is the vertical wind velocity at point M and n_x is the number concentration of X. The flux at point M is obtained by normalizing to unit area and unit time: F = n_x*w*dt*dA/(dt*dA) = n_x*w = N_a*C_x*w (since n_a*C_x = n_x) From this equation we can determine the vertical flux by continuous measurement of C and w, but because of turbulence this varies with time. However, we are only interested in the average vertical flux so we can time average this using the Reynolds decomposition and then taking the time-average, giving: Fbar = n_a(bar)*(C*w(bar)+C'*w'(bar)) The first term is the mean advective flux driven by the mean vertical wind wbar. The second term is the turbulent flux driven by the covariance between C and w. The mean wind is generally very small relative to w' because atmospheric turbulence applies equally to upward and downward motions. In the troposphere, the turbulent flux usually dominates in determining rates of vertical transport.
In the evolution of the Earth, how did N(2) end up as the most abundant gas in the atmosphere?
When the Earth was formed through gravitational accretion, the Earth was highly volcanic due to the energy released in its interior by radioactive decay and gravitational accretion. Volcanic plumes show a composition of the outgassed material as 95% water, CO(2) and N(2), and sulfur gases. There was no O(2); volcanic plumes contain only trace amounts of O(2). Examination of the oldest rocks on Earth show that they formed in a reducing atmosphere devoid of O(2). The outgassed water precipitated to form the oceans. CO(2) and sulfur gases then dissolved in the oceans, leaving N(2) as the dominant gas in the atmosphere. The presence of liquid water allowed the development of living organisms. Early organisms developed the capacity to convert CO(2) to organic carbon by photosynthesis. This process released O(2) which gradually accumulated in the atmosphere; reaching its current concentration about 400 million years ago.