WEATHER Archives | Math for Grownups

In Math at Work Monday

Welcome Sandy! Meteorology and math

Things are looking bad for those of us in Hurricane Sandy’s path. Like most of my neighbors I spent the weekend cleaning up the yard and cleaning out the local grocery stores. But one thing is certain: In a short while, my electricity will be out, and I can expect to be living like Laura Ingalls Wilder in the city for at least a few days. That means no computer, no internet.

So for part of this week, at least, I’m bringing you some topical (not tropical!) highlights from posts past. First up is my interview with on-air meteorologist, Tony Pann. Here’s how he uses math in his work. (I’m betting he’s pretty darned busy this morning!)

Math at Work Monday: Tony the on-air meteorologist

Tony Pann is an on-air meteorologist for WBAL-TV 11 in Baltimore, Maryland.

I have been a television meteorologist for 22 years. Since 2009, I’ve been working as part of the morning team at WBAL TV.

When do you use basic math in your job?

I use math everyday! The computer models that we use to forecast the weather, are based on very complicated formulas derived from fluid dynamics. The atmosphere acts very much like a body of water, so the same mathematics can be applied to both. Each day, over a dozen different computer models are run predicting the state of the atmosphere at different time frames. An initial set of data is entered at a specific starting time, then the model shows us it’s interpretation of what the state of the atmosphere will be at certain time intervals. For example, the data might be entered at 7 a.m., then the model will predict the temperature, wind speed, and barometric pressure at 10 a.m., 1 p.m. and 4 p.m. Some of these models are short range, and only extend out to 48 hours, while others go all the way out to 365 hours from the starting point!

So let’s say there are 13 models that do this same thing each and every day, two or three times a day. It’s my job as a meteorologist to interpret all of that data, and translate it into the very understandable and reliable seven-day forecast that you see on TV. With so much data out there, the intuition and experience of the forecaster is very important. Since each model takes in the same starting data, but is run on a different formula, they all come up with different answers. For example, one model might say the high temp for today is going to be 45 and another could say 50. Or one could predict 6 inches of snow and the other says 1 inch. It’s my job to decide which one is right and why.

Sometimes I don’t trust any of them, and I’ll do a quick calculation on my own. Here’s an equation that I can use to calculate the high temp for the day by hand:

I then go on TV, and try and explain it all in an interesting manor — at least that’s the goal.

Did you have to learn new skills in order to do the math you use in your job?

In order to get a degree in meteorology, you actually have to learn all of the math that the computers are doing to give us those answers. It’s not easy! By the time we are finished, we’re just a class or two short of having a minor in mathematics. It’s great to know what the computers are doing, but I’m glad we don’t have to work it out by hand anymore. If not for the wonderful training in the world of mathematics, I most certainly would not be doing this job.

Do you have questions for Tony? Ask them in the comments section, and I’ll let him know to peek in! He’ll be a bit busy for a while, so be patient!

In Current Events

How Hot Is It? Calculating the heat index

Lordy, it’s hot. And the heat makes me cranky. When I saw that the temps were creeping up to the 90s and beyond this week, I vowed to stay in the airconditioning. Trust me; it’s best for everyone involved.

So don’t even tell me what the heat index is. I really don’t want to know. But I have always been fascinated with how it is calculated. What are the variables that affect the heat index? Let’s take a look.

The heat index is how it really feels when the humidity is figured in. (Those of you who live in a climate with dry heat have no clue about this. Count yourselves lucky.) When the humidity is high, the heat index goes up, producing a hot, sticky mess that makes my hair frizzy and sours my otherwise lovely temperament.

The thermometer may say 95 degrees Fahrenheit, but if there’s significant humidity, it might feel like it’s 105. But of course meteorologists don’t guess at this number. There’s an actual formula that’s used to find the heat index.

Before we get to that, let’s consider the variables involved. According to the National Oceanic and Atmospheric Administration (NOAA), there are 20 (yes, twenty) variables that are used to calculate the heat index. These range from vapor pressure to the dimensions of a human to ventilation rate to sweating rate (ew). Because most of these are very specific to each person, a mathematical model was used to determine an appropriate range for each. This allows meteorologists to use a (relatively) simple formula for finding the heat index:

HI = -42.379 + 2.04901523T + 10.14333127R – 0.22475541TR – 6.83783(10^-3T²) – 5.481717(10^-2R²) + 1.22874(10^-3T²R) + 8.5282(10^-2TR²) – 1.99(10^-6T²R²)

Pretty, right? It’s actually not that hard to understand, if you break down the pieces. First, let’s define the variables.

HI = heat index

T = ambient dry bulb temperature (in Fahrenheit)

R = relative humidity (integer percentage)

So there are basically three variables, one being what we are looking for — the heat index. If you were to use this formula, you would need to know two things: the ambient dry bulb temperature (which is merely the ambient temperature as measured by a thermometer) and the relative humidity.

If you put to work the logical part of your brain that notices connections and patterns (yes, you do have one), the math becomes clear. When the temperature and relative humidity go up, so does the heat index. How do you know that? Look at the equation. It’s full of addition and multiplication. In fact, aside from the negative exponents (which actually yield smaller numbers), the equation is based solely on increasing values.

(That is, unless you have negative values for T and R. But in that case, you wouldn’t be figuring the heat index, right? A negative T means a negative air temperature, which is really cold in Fahrenheit. And I’m not sure that relative humidity can be negative at all.)

Now, almost nothing is absolute in weather prediction and measurement, right? And this equation is no exception. As NOAA points out, this equation is created by multiple regression analysis, which means it is not exact. (Basically, in this process, the mathematicians are fitting points to the closest line. Think of a bunch of points on a graph and how you can draw a predictable line or curve that is closest to all of those points.) There is in fact an error of ±1.3 degrees Fahrenheit. But what’s 1.3 degrees when you’re looking at a heat index of 102? Either way, it’s still darned hot.

How do you manage the heat? Do you head inside or hide in a cool, dark place? Share your ideas in the comments section.

In Current Events

Using Math to Predict Hurricanes

Okay, I’ll admit it. I don’t typically watch television news. (Sorry Tony!) But when bad weather comes along, seeing those weather maps is often exactly what I’m looking for.

I lived in a hurricane prone area for 15 years, weathering (eh-hem) many a storm and getting through some close misses. When you see that many big storms, you get used to the terminology (like storm surge) and develop a false confidence in your own ability to predict what’s coming.

But as you know, a gut feeling isn’t enough. In fact, meteorologists use a complex system of previous data and what they know about how these storms act to make predictions. What they’re saying, though, is that there is a chance something will happen. And what is that based on? Probability and statistics.

In Math at Work Monday

Math at Work Monday: Tony the on-air meteorologist

Quick! What do you have to know before changing from your jammies into something a little more work appropriate? The weather, right? Tony Pann is an on-air meteorologist for WBAL-TV 11 in Baltimore, Maryland. Math helps him predict if there are sunny skies ahead or if you’ll need to pack your umbrella. Here’s how.

Can you explain what you do for a living?

I have been a television meteorologist for 22 years. Since 2009, I’ve been working as part of the morning team at WBAL TV.

When do you use basic math in your job?

I use math everyday! The computer models that we use to forecast the weather, are based on very complicated formulas derived from fluid dynamics. The atmosphere acts very much like a body of water, so the same mathematics can be applied to both. Each day, over a dozen different computer models are run predicting the state of the atmosphere at different time frames. An initial set of data is entered at a specific starting time, then the model shows us it’s interpretation of what the state of the atmosphere will be at certain time intervals. For example, the data might be entered at 7 a.m., then the model will predict the temperature, wind speed, and barometric pressure at 10 a.m., 1 p.m. and 4 p.m. Some of these models are short range, and only extend out to 48 hours, while others go all the way out to 365 hours from the starting point!

So let’s say there are 13 models that do this same thing each and every day, two or three times a day. It’s my job as a meteorologist to interpret all of that data, and translate it into the very understandable and reliable seven-day forecast that you see on TV. With so much data out there, the intuition and experience of the forecaster is very important. Since each model takes in the same starting data, but is run on a different formula, they all come up with different answers. For example, one model might say the high temp for today is going to be 45 and another could say 50. Or one could predict 6 inches of snow and the other says 1 inch. It’s my job to decide which one is right and why.

Sometimes I don’t trust any of them, and I’ll do a quick calculation on my own. Here’s an equationthat I can use to calculate the high temp for the day by hand:

T_max = (Tk_{1000 – 850}*0.36)-422

where T_max is the potential high temperature and Tk_{1000-850} is the 1000mb to 850mb thickness in meters.

I then go on TV, and try and explain it all in an interesting manor — at least that’s the goal.

Did you have to learn new skills in order to do the math you use in your job?

In order to get a degree in meteorology, you actually have to learn all of the math that the computers are doing to give us those answers. It’s not easy! By the time we are finished, we’re just a class or two short of having a minor in mathematics. It’s great to know what the computers are doing, but I’m glad we don’t have to work it out by hand anymore. If not for the wonderful training in the world of mathematics, I most certainly would not be doing this job.

Do you have questions for Tony? Ask them in the comments section, and I’ll let him know to peek in!

In Math for Grownups

Film Friday: Using math to predict hurricanes

Even if you weren’t in the predicted path of Hurricane Irene, you likely heard about pretty much nothing but last weekend. We Americans love our big storms. There’s been lots of grumbling lately about over-hyped media coverage, especially since the hurricane was downgraded to a Category 1. But this was a bad storm — big, slow moving and full of rain.

Remarkably, the storm followed the path that meteorologists predicted: hitting landfall in North Carolina and moving up the east coast, hugging the shore. How did they know?

This video from The Weather Channel gives a really good explanation.

By the way, I apologize for being absent online for much of this week. I didn’t have power until Monday, and then it took another three days for my internet connection to be restored. Hope everyone else fared well!