CE 397: Environmental Risk Assessment


Lectures 11 and 12: Atmospheric Transport Modeling






The atmosphere is generally thought of as having four major "layers" that are defined by the nature of average temperature profiles in each layer (see handout).


The layer closest to the earth's surface is referred to as the troposphere. It extends to approximately 10 km above the earth's surface. It's importance is underscored by the fact that humans emit almost all air pollution to the troposphere (exceptions?). The troposphere contains the earth's biosphere and nearly all of the atmosphere's water. It also contributes approximately 80% of the atmosphere's mass.


The troposphere can be further divided into several important layers. The layer closest to the earth's surface (of obvious importance with respect to emissions, transport and human exposure) is referred to as the planetary boundary layer (PBL). The PBL generally extends to heights of approximately 500 to 1500 m, and is often characterized as the layer through which the atmosphere "feels" the effects of frictional drag at the earth's surface. For high pressure regions over land, the PBL consists of several major parts (see handout): a mixed layer, a stable (nocturnal) boundary layer, a nd a residual layer above the nocturnal boundary layer. This residual layer contains mixed layer air from the previous daytime period.


The planetary boundary layer is characterized by a capping inversion in which temperature actually increases with height. The region of the troposphere above the PBL is referred to as the "free atmosphere". For anyone who has ever flown into Los Angeles of Mexico City you will probably recognize the transition from the free atmosphere into the far less attractive PBL!


The next major layer of the atmosphere is referred to as the stratosphere (or layered sphere). The stratosphere is characterized by a temperature that increases with height due to the absorption of ultraviolet radiation by molecular oxygen and ozone. Several of the important chemical reactions that define the thermal nature of the atmosphere are presented in the handout for this lecture. Note that the temperature gradient within the stratosphere precludes efficient vertical mixing within this part of the atmosphere. Hence, the vertical movement of pollutants occurs over very long time periods, and chemicals that migrate into the stratosphere can remain there for very long periods of time. In fact, the stratosphere is an effective museum that contains many exhibits in the form of particulate matter from past volcanic eruptions and above-ground nuclear testing!


Until recently, the stratosphere has never been thought of as a major player in environmental risk assessment. However, the depletion of stratospheric ozone may pose much greater risks to living organisms at the earth's surface than all chemicals on earth. To my knowledge (I might be wrong) there is currently no effort to link stratospheric ozone depleting chemicals with human health risks in a manner analogous to human exposure to toxic chemicals in the troposphere.


The thin layer of atmosphere that serves as a border between the troposphere and stratosphere is referred to as the tropopause. This region is defined by rapid reductions in turbulent kinetic energy and water vapor, and increases in temperature gradients and ozone concentrations.


The final two layers of the earth's atmosphere include the mesosphere and the thermosphere. For purposes of environmental risk assessment, these layers are of little interest (although they may be 200 years from now!).



4 Environmental (Ambient) Lapse Rates


As described above, atmospheric temperature gradients play a major role in defining the nature of pollutant mixing/dispersion in the atmosphere. By convention, we typically take the negative of a temperature gradient and refer to this as a "lapse rate". The lapse rate that generally defines the nature of pollutant mixing is the environmental (or ambient) lapse rate (Ge).


The environmental lapse rate is defined simply as the negative of the actual vertical temperature gradient:


Ge = -{dT/dz}e


Here, the temperature gradient can be thought of as the change in temperatures that would be measured by a thermometer at different heights above the earth's surface. The average value of Ge in the troposhere is 6 - 7 C/km. However, it is VERY IMPORTANT to note that Ge can (and does) vary is both time and space.




The dry adiabatic lapse rate (Gd) is defined as the rate at which the temperature of a dry "parcel" of air would change (with height) as it is expanded with upward motion or compressed with downward motion in the absence of heat transfer with its surroundings.


Unlike the environmental lapse rate, the dry adiabatic lapse rate is always a constant. It's value can be derived by application of the ideal gas law, barometric equation, the first law of thermodynamics, a couple of shots of rum. Your instructor has used these methods to derive Gd as shown in the handout for this lecture. The end result is that Gd is the ratio of gravitational acceleration (9.81 m/s2) and the specific heat of air at constant pressure (Cp = 1004 J/deg-kg), i.e., Gd = 9.8 deg/km.



4 Atmospheric Stability


Atmospheric stability can be defined qualitatively as a measure of the degree of vertical mixing in the atmosphere. An alternate definition is "the atmosphere's tendency to dampen or enhance vertical motion." Atmospheres that are poorly mixed in the vertical direction are said to be "stable". Conditions of extreme stability may be associated with either elevated or ground-based inversions. Atmospheres that have significant vertical mixing are said to be "unstable" (like the less computer-oriented of your two professors in this course!). Those atmospheres of moderate vertical mixing are often said to tend toward "neutral stability".


The spectrum of atmospheric stabilities is generally thought of as being directly related to the amount of turbulent kinetic energy (TKE) in the atmosphere. This TKE is generated by two basic mechanisms: (1) mechanical shear caused by air flow over the earth's surface and (2) buoyancy-induced vertical acceleration of air. The first mechanism becomes more important in the near vicinity of the earth's surface, and is generally the dominant mechanism for stable and neutral stability conditions. Buoyancy-induced turbulence generally leads to the greatest amount of vertical mixing in the atmosphere and is associated with hot, sunny days. This mechanism gives rise to thermal (convective) updrafts and downdrafts. Jonathon Livingston Seagull was known to take advantage of updrafts as he soared to great heights (or was that Timothy Leary --- it's getting late).


Note that at any time the troposphere can have zone that vary significantly in terms of stability. The extent of stability in any zone can be quantified as the difference in environmental and dry adiabatic lapse rates (your instructor will explain why in lecture - a pictorial example is provided in your handout).


If one defines a "degree of stability" (S) as:


S = Gd - Ge


It can be reasonably argued that the troposphere (or some zone within the troposphere) becomes more unstable as S becomes more negative, more stable as S becomes more positive, and should approach neutral stability as S approaches zero.



4 Plume Type


The spatial and temporal variation of Ge relative to the constant Gd causes significant variations in the nature of pollutant transport downwind of a source. Several plume types will be discussed in lecture. Examples of the effects of Ge on plume behavior are provided in the accompanying handout.


From the standpoint of environmental risk assessment it is important to recognize that maximum concentrations for ground-level releases will occur during periods of lowest vertical mixing. These conditions exist for ground-based (nocturnal) inversions that occur on clear nights. For such conditions, Ge is negative and S > 9.8 deg/km. If one desires to model a "worst-case" scenario for a ground-level release, e.g., associated with a chemical spill or out-gassing from soil, stable nocturnal conditions should be considered. For the case of out-gassing soil, this condition may also be one where emission rates are greatest due to barometric pumping (expansions in gas volume due to nocturnal reductions in barometric pressure).





4 The Atmospheric Diffusion Equation


The gaussian plume model (gpm) can be derived from either a Lagrangian or Eulerian frame of reference. Your instructor has tried to derive the gpm from a Lagrangian viewpoint and has repeatedly failed miserably.


From an Eulerian framework, the starting point for derivation of the gaussian plume model is the decomposed and averaged advection-diffusion equation with first-order closure (see handout). The resulting equation, which contains a first-order (gradient) approximation for terms involving the product of fluctuating concentrations and velocities, is referred to as the atmospheric diffusion equation. Although it represents an approximation of reality, it is where any sense of reality ends in terms of our conventional methods for estimating atmospheric dispersion. Hence, I introduce the gaussian plume model.



4 Major Assumptions


In order to understand the enormous uncertainties associated with the gaussian plume model, one should be introduced to the many simplifying assumptions made in its derivation. Several major assumptions are listed below and are described in the accompanying handout.


(1). Steady-state conditions.

This assumption requires that concentrations at all points in space are constant with time, i.e., local meteorology and source strength are constant. For most situations such conditions are never true. However, they may be reaonaably approached over short time periods (say 1 hour or less).


(2). Wind blows in x-direction and is constant in both speed and direction.

(3). Transport by mean wind >> turbulent transport in x-direction.


(4). The source emission rate is constant (Q).


(5). Eddy diffusion coefficients are constant in both time and space (BAD).


(6). The source emits pollutants at x = y = 0 and z = H (effective stack height).


(7). Inert pollutants (this is sometimes modified by assuming a simple first-order decay).


(8). There is no barrier to pollutant transport above or below the plume. This is usually acocunted for in a somewhat demented way (to be discussed in lecture).


(9). Mass is conserved across a plume cross-section.


(10). Mass within a plume follows a gaussian distribution in both the y (crosswind) and z (vertical) directions. This is often a reasonable assumption for the y-direction. However, it is generally a terrible assumption for the z-direction, particularly for ground-level releases, i.e., those that are often of interest with respect to environmental risk assessment.


When all is said and done, these assumptions can lead to very significant errors in predicted emissions. In general, if one is interested only in maximum ground-level concentrations downwind of a point source (independent of location), the gaussian plume model should provide results that are within a factor of two or three for all but highly unstable conditions (in which case one must as well punt). When concentrations are required at fixed locations, uncertainties in model predictions are magnified and may be greater than an order of magnitude depending on specific meteorological conditions and source-receptor orientation. The bottom line is that one should take great caution in representing predicted concentrations with any more than one significant figure! We can do better with more advanced models that require meteorological data that are generally not available at most airports or other weather stations.


4 Point-Source Gaussian Plume Model


See accompanying handout for a presentation of the simplest point-source gaussian plume model with no barriers to vertical transport. Particular attention should be given to the various terms that comprise this model.


4 Point-Source Gaussian Plume Model with Reflection


See accompanying handout for a revised version of the point-source gaussian plume model that accounts for perfect reflection at the ground surface.


See handout for a description of several special cases associated with the gaussian plume model. Of particular interest with respect to environmental risk assessment are the cases of ground-level sources and/or ground-level receptors.


4 Wind Speed and Direction


The way that wind speed is treated in the gaussian plume model leads to very significant uncertainties. Most meteorological stations record wind speeds at 10 m above the earth's surface. However, most emissions are at heights other than 10 m. Since wind speed (AND DIRECTION - see photos in lecture) can vary significantly with height, an adjustment must be made to measured wind speeds. Such adjustments are generally empirical and fraught with uncertainty. The most appropriate method for accounting for vertical variations in wind speed would be to include a functional relationship between wind speed and z. This can not be accomplished given the structure of the gaussian plume model but can be accomplished using gradient transport (K-theory) models. This is a major advantage of k-theory models over gpm, especially for ground-level or near ground-level releases.


4 Dispersion Coefficients


Estimation of downwind concentrations requires values for the horizontal and vertical dispersion coefficients. Methods for estimating these parameters will be discussed in lecture. Of critical importance are the limitations associated with conventional curves generated from Project Prarie Grass (the Woodstock of Meteorology), and slight improvements made by G.A. Briggs in the 1970s.



4 Plume Rise

This is a critical parameter for estimating maximum downwind concentrations. In general, maximum ground-level concentrations are inversely proportional to the square of the effective stack height. Thus, factor of two errors (not uncommon) in estimates of effective stack height are associated with a factor of four error in concentration measurements. Dozens of researchers have presented empirical relationships for estimating plume rise. For similar conditions, these relationships can yield order of magnitude differences in predicted plume rise.



4 Maximum Ground-Level Concentration


It is often important to know maximum concentrations downwind of a source. The location and magnitudes of thee concentrations can be determined mathemtically. This has already been done for you and is provided as a set of curves (see handout).



Highways, waste ditches, etc, are often modeled as line sources by integrating the gpm over appropriate bounds and including a source strength that varies with distance along the source. We will discuss this concept in lecture. See Connie for additional insight.



Hazardous waste ponds, off-gassing soil, etc. are often modeled as area sources by integrating the gpm twice over appropriate bounds and including a source strength that varies in two-dimensional space. We will discuss this concept in lecture. See Malcolm if you have further questions.



4 Time Averaging


I think that it is time for me to go home. See you in lecture.