# Modelling uncertainty and errors

by Barry
(Calgary)

Gauss

Here is what the EPA has to say about modelling uncertainty and errors. It incorporates some theory put forth by Carl Gauss:

Modeling software is more trustworthy for coming up with longer time-period concentrations than for calculating one-hour concentrations at precise locations.

The programs are okay for estimating highest concentrations that may take place anywhere in the domain. For example,
"...errors in highest estimated concentrations of ± 10 to 40 % are found to be typical (assuming appropriate inputs)."
Calculations of concentrations at an exact time and place don't correlate well with monitored concentrations (corresponding to the same time and place) and reliability isn't as good.

There are two types of uncertainty:

1) Reducible - where plume locating errors arise from errors in wind direction in the meteorological data.

2) Unspecified uncertainties in the atmosphere.
These errors can be big, up to 50%, but they don't mean specific concentrations don't exist.
These are examples of natural modeling uncertainties. It's hard to tell exactly when and where.

## What does Gauss have to do with air pollution?

Today we're diving into a fascinating topic that helps us understand the world around us - Gaussian statistics. Let's break it down and make it as clear as a sunny day, so don't let those fancy words scare you off!

Gaussian statistics are like a snug-fitting jacket. Isn't it great when your jacket fits just right? That's kinda how Gaussian statistics work. It describes how things tend to cluster around an average or 'central' value. Throw a bunch of darts at a target - most of them hit the bullseye. Not when I'm throwing but you get the 'point'.

How does this relate to air quality modelling? What a great question! Think of a big city with lots of cars, factories, and other things that release pollutants. Pollutants don't just stay in one place - they spread out, creating a pollution cloud.

We can predict how this pollution cloud will move and disperse with the help of air quality modeling. Guess what? Pollutants often spread in this Gaussian pattern. Like fading ripples in a pond after you throw a pebble, the highest concentration of pollutants is usually near the source - such as a busy intersection with lots of car exhaust.

We can make some really cool predictions using Gaussian statistics and air quality modeling. It's possible to estimate how pollution levels might change over time, where it might travel, and even how it might mix with clean air around it. How different winds change the distribution. It helps us understand potential health risks, plan better urban designs, and improve air quality.

Whether you're trying to hit the bullseye on a dart board or figuring out how pollution moves through the air, Gaussian statistics and air quality modeling are your trusted tools. This first part describes general dispersion around a ground-based source of emissions.

We may technically refer to these as "fugitive emissions." But here's something different...a PLUME.

## Look at a stream, like smoke coming out of a chimney.

Let's say you're standing by this bonfire, and the wind is blowing your way. You can feel the heat of the flames on your face and smell the smoke drifting toward you. What if you stepped to the side? There's less heat and smoke now (but still more than none). In the world of air quality, this shift is similar to plume centerline and dispersion.

The plume centerline is like the path smoke follows from the fire. It's like Hansel and Gretel left breadcrumbs. Whenever a plume rises from a factory chimney or car exhaust, it may follow a well-behaved road. That's what scientists call a centerline.

Here's where it gets interesting - dispersion. Plumes don't stay narrow forever. As one travels, a plume spreads out and dances around. This happens because the air itself isn't stationary and neither is it flowing perfectly straight - it's constantly swirling, changing, and moving.

Imagine throwing confetti in the wind. As the confetti pieces ride the currents, they spread out, creating a beautiful, colorful pattern in the air. Some might go straight downstream, others twirl around. Pollutants in the plume mix and mingle with the surrounding air, creating a complex dance.

In general, pollutants stay near the plume centerline for a while, but dispersion adds an interesting twist. The air becomes the stage and the pollutants are the performers in this mesmerizing choreography of nature.

As you get further away from the source, the plume spreads out. So there's eventually a lower concentration everywhere in the plume (including the centerline) than it would be up close to the smoke stack. Concentration also gets lower as you move away from the centerline, which changes position with the wind.

Understanding plume centerline and dispersion helps us understand air quality. This helps us predict where pollutants will end up, how they'll spread, and what areas might be affected. The air quality can change depending on the wind, the landscape, and even the time of day, just like a bonfire.

The next time you see smoke swirling from a chimney or exhaust from a passing car, remember there's a symphony of movement in the air, a dance of particles influenced by tiny invisible currents.

### Comments for Modelling uncertainty and errors

Average Rating

 Rating math by: Anonymous Why have a picture of gauss if your not going to really go into his math?From Barry - His work has had a great impact on many fields, including physics and engineering. Gauss is widely considered one of the most influential mathematicians in history. A picture of him can serve as a reminder of his contributions and how important he was.A page full of equations would turn most people off. Wikipedia gives an introductory look at his distribution principles. But some people will find it very technical.https://en.wikipedia.org/wiki/Normal_distribution

 Rating Interesting by: Anonymous An interesting analysis. I'll have to look into it closer. thanks. From Barry - I'm sure more useful info can be found online. Check Wikipedia for an introduction:https://en.wikipedia.org/wiki/Atmospheric_dispersion_modeling

 Rating Looked good, by: Diane First impression of the page was that it looked good, and loaded fast, as for the content i did not understand any of it.From Barry - It's probably because the content is too complex for most people. Readers who have had a few math or physics courses or do more research will better understand the concepts. Dispersion theory is quite specialized.

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