Grr… a pre-note.  I had thought I posted this yesterday but apparently I only saved it as a draft.  Hitting Publish instead of Save helps.  Now on with it.

It’s difficult these days to pick up a newspaper or watch the news without hearing at least one piece of news about the pollution problems in this world.  Whether it’s about the Kyoto Treaty, An Inconvenient Truth, Global Warming, or gas prices, it’s a terrible trend that sadly, is likely to continue.  Just the other day I read (here in Seattle) about a group of students that are riding their bikes across the country trying to spread global awareness of carbon dioxide emissions.  It’s called “An Inconvenient Ride” Pretty catchy, but maybe beside why I’m writing.  Or is it?

Truthfully, this is a scientific computing class and I’ve mentioned this example to really show how important this pollution topic has become to people so one question that comes to mind is how are we to predict and model the ever growing pollution in this world?  Well scientific computing is the first step but here’s a little more detail on how’s it’s being done now and maybe where it will go.

In Computational and Numerical Challenges in Environmental Modeling, Zlatev and Dimov describe in the introduction at a high level about having to use PDEs and ODEs to first even initially calculate pollution models, which usually involve one equation per chemical in the air.  This already is becoming a relatively large problem with already massive datasets (perhaps going back 10 years or so) and then on top of that having to run multiple simulations to really see if these models can be accurate or not.  This means we need fast computers and massive amounts of storage space to even begin doing these computations.  Solving these PDEs and ODEs is no easy task either, but as we’re doing in class, numerical methods must be used to solve these systems of PDEs and ODEs.   This book goes into more advanced ways of trying to solve these systems by discretizing and somehow splitting these equations up to more easily calculate the answers, but the mathematics involved in that is far and away beyond the scope of this class, much less this blog post.  There’s also a chapter dedicated to just doing efficient matrix computations depending on what inputs are used and the algorithms associated with them.

This splitting of systems though means that there’s an additional efficiency that we can add into these computation methods: parallelizing.  In both this book and another article on this subject, both talk about how to do this and how important it can become.  One major hurdle though is actually implementing this and doing it efficiently.  The problems that come with having multiple processors to do the job is how difficult it is to control and do this efficiently and this technology is still being developed as quad core processors have hit the market in only the past few months.  Therefore the complicated architecture is really holding this back.

Most importantly though, the question arises of whether our current methods are enough.  Zlatev and Dimov both most definitely say no.  Smaller problems can more easily be studied, but these are the problems we can solve now and on a whole does not really tell us much on what’s going on in our environment completely.  Then another consideration is if whether it’s possible or not to calculate and simulate these systems without the use of splitting.  Splitting up these equations imparts an amount of error which may actually be too much to accurately portray the environment in some cases.  But it’s better to try to get something mostly accurate than nothing at all right?  That’s why the argument of better parallel computing can be made in this case and that’s why we need to figure out more efficient ways to compute large systems of equations.

Sources:

http://books.google.com/books?id=7JYobsd9iDEC&pg=PA1&lpg=PA1&dq=Air+Pollution+PDE&source=web&ots=UPH0rPabIu&sig=dH-uorCg1lrTxcggMhQYJFEn3Wg&hl=en#PPR16,M1

http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V12-44B2DXJ-D&_user=10&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=41962fefe1ce2169656810b4bafcffda