Jeffries' group at UNC and Michael Gery, Atmospheric Research Assoc., Boston MA (ARA) have created a new kind of representation for organic species in air quality model photochemical reaction mechanisms. In addition to the normal molecules that appear in such mechanisms, we have introduced reaction entities that have dynamic character or properties throughout the simulation; we call these new entities "morphecules" (the molecules in our mechanism have static properties). In all presently used chemical species representations, the only state memory is species concentration, and thus adding more detail to the representation has involved increasing the number of species. Adding new species, however, increases the number of ordinary differential equations (ODEs) that must be solved to make predictions with the reaction mechanism. The difficulty of solution of the coupled ODE system increases at approximately the cube of the number of species, so increasing the number of species to obtain more representational detail is computationally expensive. The Carbon Bond Four mechanism, presently used in SAQM, has only 12 organic species that are input to represent the urban atmosphere.

What's an Allomorph?

In our representation, we provide additional state memory in the form of "allomorphs" and their properties. An allomorph is a variant on a morphecule's shape, and it may be an explicit molecule or it may itself be of surrogate or lumped character. For example, if the morphecule is N-ALKANE, its allomorphs would be the explicit species N-C2H6, N-C3H8, N-C4H10, ... N-C9H20 and the properties of the morphecule would be computed by weighted sums of the properties of the allomorphs. The allomorphs are not represented by ODE equations, only the N-ALKANE species.

How does it work?

The numerical solution of the coupled sets of ODEs arising from a chemical reaction mechanism is produced in time by a "marching" technique, in which the system state is advanced from a given state at time t to another state at time t+h, where h is a small time interval. In our morphecule representation, we keep the morphecule properties, which were determined "before" the time step from the initial state of the associated allomorph's properties, constant over this small time interval. "After" the time step, we can determine the change in morphecule concentration, as well as determining an effective average production and average loss rate for the morphecule applicable over the interval. These average properties over the one time step can be used with the specific allomorphic properties in a set of linear equations, to partition the change in the total morphecule concentration into changes appropriate for each of the morphecule's associated allomorphs as well as to transfer the change in reactant allomorphs to product allomorphs that are consistent with the change in the product morphecule's concentration. Thus, ODE equations have been turned into linear equations and the work to solve the latter is significantly less than the work to solve the former. This "before" and "after" computation occurs on every chemical time step and thus the loss and production of the allomorphs, while being computed by a linearized process can closely approximate the behavior of a fully coupled ODE solution in which allomorphs replace morphecules, but at significantly less computational costs. The range of the allomorphs associated with each morphecule is limited by how differently the extreme allomorphs might react over one time step. Furthermore, because these additional computations take place before and after the ODE solution step, no changes need be made to the conventional ODE solvers in the models.

In the currently used chemical representations in air quality models, the properties of the "lumped" or "surrogate" species are held constant for the entire simulation. Even if the initial properties of the principle reacting organic species were computed dynamically from time step to time step and were permitted to vary over the domain, the existing modeling methods lose all such detail after the first reaction. This is because the reaction products--being static entities with constant properties--do not capture the initial variation. Product species must also be morphecules.

What is Morpho?

The morphecule/allomorph representation introduces the need for vector and matrix variables into the mechanism description as well as a need for a convenient packaging of the associations between morphecules and their properties and the allomorphs and their properties. To support this more complex representation, UNC has developed a complete computer language with a formal grammar that we call Morpho. This language is translated into computer codes by an infinite lookahead, recursive-decent compiler program; a variety of output formats can be produced, eg, one for a virtual calculator that is part of a companion chamber simulation modeling program, and another that is in the form of standard FORTRAN or C subroutines for compiling and linking into Eulerian models. The compiler and solver were designed using object-oriented design methods and were implemented in C++ using the ANSI Standard C++ Library. They are highly modular, fully expandable, and well documented using object oriented techniques. There are no "hardwired" runtime limitations (ie, maximum species name length, maximum number of species and reactions, etc) as all storage management is dynamic. The codes compile and execute on multiple computer platforms including PPC Macintosh, Windows95/NT, and UNIX. The compiled format of the mechanism is platform independent and a mechanism can be compiled on a PC and solved on a workstation.

In addition to representing chemical species as either molecules or morphecules, the Morpho language permits the user to declare and use scalar, vector, and array variables with generalized mathematical operations among these variables and species properties including dot product and scalar-vector, vector-vector, and scalar-array, vector-array operations. Time and species varying stoichiometry, reaction rate constants, gas law calculations, and the use of bulk species and physical conditions properties (temperature, pressure, humidity) are all easily expressible in Morpho. Complex species names are also possible, for example,

'C-C(O)-C=C(C)-C(ONO2)C(C)(OH)-C(O)'

as there is no limit to the number or type of characters that can be included in a species' name.

What's the status?

Beta-level compiler and gear-based solver codes have been completed and tests of system performance has started. At present these are command-line tools, but platform independent Java applications are being designed to provide a graphics user interface to both the compiler and the solver. A client/server architecture is being developed to permit the modeling system to be remotely operated over the internet.

The design and creation of a morphecule reaction mechanism for urban atmospheric simulation is under way by Mike Gery and Roger Atkinson that will incorporate the current state of the science knowledge about reaction processes. A mechanism for five classes of alkanes, each with 5 to 10 allomorphs, organic peroxy and alkoxy radicals with 12 allomorphs, aldehydes (7 allomorphs), ketones (6 allomorphs), four classes of alkenes (19 allomorphs), three di-functional peroxy radicals (13 allomorphs), one alkyl-substituted benzene (7 allomorphs), alkyl-epoxy-benzene (20 allomorphs), alkyl-phenols (4 allormorphs), 2,4-diene-1,6-dials (20 allomorphs), and 1,4-unsaturated dials (10 allomorphs) has been assembled and rate constants and structural reactivity relationships are being developed. This mechanism will be tested against observed smog chamber data from as many as 6 chambers.

At the least advanced end, a new ARA/UNC mechanism without any morphecules would represent an advancement in the quality of a standard one-species one-ODE approach by taking advantage of some of the more advanced mathematical representations and by incorporating the latest knowledge about kinetics and mechanistic pathways. At the most advanced end, a ARA/UNC mechanism with full use of morphecules will permit comparison of model predictions at nearly the fully observed detail of ambient hydrocarbon speciation yet would not be much more computationally costly than the latest SAPRC-type mechanism. We can formulate and generalize at any level of detail between these two.

What's in the future for morphecules?

Finally, UNC and MCNC are also exploring an "adaptive chemistry" approach to be used with adaptive or nested grid Eulerian models. In most multi-grid Eulerian models, the same chemistry is used in all grid cells resulting in a lot of overhead to solve for totally un-important species in both the course and fine grids of the models. In the "adaptive chemistry" approach, we would use a fixed number of morphecules every where in the modeling domain, but would vary the distribution of allomorphs to morphecules depending upon the grid resolution. In the high resolution domain, over the reactive urban centers, we would allocate only a few morphecules to hold the mass of the slowly reacting (but usually large mass) species, while using most of the morphecules to represent the fast reacting species being emitted in the urban areas. In the low resolution domains, away from major emissions, we would allocate only a few of the morphecules to hold the "dregs" of the reactive urban species and would spread out the more slowly reacting, but now dominate species over the majority of the morphecules. UNC's process analysis techniques can be used to compute a balance of process rates at the interface of these two mechanisms and the re-distribution of allomorphic mass would be done to maintain the same process rates across the interface. In this way, the limited number of ODE species in large scale regional/global models could be used to maximum representational advantage and more accurate chemical transformation rates would be computed in both the low and high resolution portions of the model domain.

A pdf file of this introduction is available for download here.

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