This would be something like the method of characteristics for the advection part, if I am not mistaken?I do not see the connection to the model for the parameter of the advection then. Could you please elaborate? Quote:"Like lowlands (e.g. Heimay) versus uplands(Vatnajukell) wind profiles?"I would like to ignore location-specific characteristics and picture only the "stylized facts" I listed below.

Maybe MOC is not such a good idea after all. It probably has more to do with the PDE than wind data.

Yes, but for the PDE it is indeed the best choice (in my non-expert opinion). Thanks.

The PDE is solvable. It is in conservative form in diffusion(yes?).What is the relationship between {u1,u2} and the Weibull? Does Weibull sampling deliver the u1, u2 data for the PDE?

yes, conservative.wind speed = sqrt(u1^2 + u2^2) over a year is Weibull distributed. (which does not mean that the (acculumated) time series process does have a weibull distribution, according to my understanding, this is Alan's "infinitely divisibility" and even more)In order to get u1 and u2, I also need the direction then.But as I said, I am open to suggestions, if you can think of another way..?

I'm not a fan of it, but people such as Philip Chatwin (who died in 2010 from Sheffield University in the UK) use very simple models to model dispersion of contaminants (I once saw him give a talk on modelling the release of a poisonous gas and I asked him if he could tell me where the gas would go, and his answer was along the lines of "yes, if you tell me the distribution", and I had a mental image of FEMA contacting him about a fire in a chemical plant and asking him if they should evacuate a town and he replying by asking them to go and measure the distribution)."Turbulent Diffusion" is the phrase they use

QuoteOriginally posted by: KnutSchnuteyes, conservative.wind speed = sqrt(u1^2 + u2^2) over a year is Weibull distributed. (which does not mean that the (acculumated) time series process does have a weibull distribution, according to my understanding, this is Alan's "infinitely divisibility" and even more)In order to get u1 and u2, I also need the direction then.But as I said, I am open to suggestions, if you can think of another way..?Seems to me that you will need u1(x,y,t) and u2(x,t) at all (x,y,t) grid point for use in the PDE. Taking Weibull samples is probably necessary but you will need to simulate wind speed on a line of x's and y's for each time in your yearly data, yes?

@Cuchulainn: As I described below, I want to keep things simple as a first shot and assume u1(x ,y,t) = u1(t) for all x,y (same for u2). Even with that assumption I find it difficult to incorporate the characteristics I want.

outrun, thanks for the suggestion. I think there are huge amount of data available (NCEP), right?If you are working on it, could you suggest a model that allows for the effects I described below?(I only use windspeed as the advection parameter in an advection diffusion equation)

Outrun,thanks for your demotivational post! :-)I did not know about the hairy ball theorem, but I guess it does not apply if I am just modeling a certain region...If you have any suggestions on literature about the infeasibility of wind modeling, you would help me out a lot. (I assume there is none though, given that published results are almost always positive).

The purpose of the PDE is to compute ash concentration based on given parameters such as advection (wind) and diffusion functions? So there are two issues, i.e. wind compute and concentration compute.Knut,I am almost sure that someone somewhere must have tackled this problem (?)