# Category Archives: climate modeling

## Just found TERC and a program for HS teachers

I look around the internet now & then to try to keep up with who else is providing useful resources for high school and college teachers who want to deal with math, modeling, earth science, climate, etc., and I just found something new that is worth sharing:

TERC EarthLab Partners

The Science Ed Resource Center at Carleton is one of the places I check in on, and I just saw the page linked above. They're looking for HS teachers who can teach the Climate Detectives module, which has 6 sessions clocking in at about 600 minutes of class time, and 1) have a colleague observe a session, 2) have students take a post-module test in 2 weeks. The aim is to improve the module for others. Look at the webpage for more details -- this is just my quick summary to give you an overview. TERC will also pay HS teachers who can participate a small honorarium to compensate some of your prep time, as well as a materials allowance.

You'll need computer lab space and computer lab resources for your students (Flash, Excel, RealPlayer or other media player). You'll also need some support from your principal and students/their parents. And you'll need to do the whole thing before May 15, 2016.

The Climate Detectives module does look cool: it talks about cores (those long strips of earth or ice drilled out by scientists) and Milankovich cycles (large-scale cycles from the wobble of the Earth, etc., which I mentioned once in a discussion of climate modeling) and geologic time and particle sizes for sand and mud. Very sciency, but with a lot of use of data. Advertise to friends and colleagues! Be a guinea pig for climate science teaching!

Feel trapped by boring fake word problems in your math textbook? Get intros to real-life issues in the natural world and see math at work.

* = required field

## How to survive a climate catastrophe

How fun to see something on the Scientific American Blogs that is so appropriate to what we've been writing about! The writer, Zev Brook, is a high school student entering 12th grade:

How to survive a climate catastrophe

Alright, he doesn't really tell us how to survive a climate catastrophe, but the first half is a nice story of the science around the Paleocene-Eocene Thermal Maximum, something mentioned briefly by the speakers during the conceptual climate models seminar as a topic they would have loved to discuss. Something Zev Brook mentions was brought up by the speakers in the final Q&A session, too: the earth is going to survive almost anything we do just fine. It's ourselves we have to worry about.

## Snowball earth... last talk at climate model summer course

These are notes from the last talk of the MAA North Central Section-sponsored summer seminar on conceptual climate models. This talk by Anna Barry tied together all the things we'd learned about over the past two days in discussing the snowball earth hypothesis, which tries to explain some mysterious pieces of paleoclimate evidence, and whether or not there is a mathematical basis for the idea.

So, let's get started!

### What could initiate a snowball earth state?

Ice-albedo feedback, which we discussed earlier (more ice -> higher albedo (more reflectivity) -> less energy in, as more solar energy is reflected -> colder -> more ice).

## Understanding climates past: more from the summer seminar

More notes from the MAA-sponsored North Central Section summer seminar on conceptual climate models. This is from Richard McGehee's talk on understanding the climate of the past and the Milankovitch cycles. These notes give some overview, but the graphs are really important to understanding these ideas and I will work on finding some to include.

Some thought-provoking questions: If we can’t even predict the weather, how can we predict the future? If we don’t know about the climates of the past, how can we expect to predict the future? The question is somewhat controversial: some climate modelers feel we only need to understand today and then we can play it all forward using big general climate models.

### How do we know the climates of the past?

Lake Vostok, Antarctica. 2.2 miles of ice on top of a tiny little pool of water down near the earth. Scientists have taken core samples from here and “gone back in time.” “Isotopes in the ice are proxies for past atmospheric temperatures above the Antarctic”: Continue reading

## Greenhouse gases: more blogging from MAA-NCS climate course

Jim Walsh from Oberlin opened today by talking about greenhouse gases and energy balance equations. His slides are online -- check them out for all the great pictures I have not included!

First big conceptual point: global climate is determined by the energy in minus the energy out. Since energy in is basically the insolation ( $Q$ -- incoming solar radiation) that is not reflected (multiply by 1-albedo) and energy out is OLR (outgoing longwave radiation) these are the three factors to look at -- change in insolation, albedo, or OLR. If these are changed by our human activities (or anything else!) climate will change.

#### Energy balance and greenhouse gases

Radiation is characterized by its direction of propagation and frequency $\nu$ . We need to know about electromagnetic spectrum, and for climatology (look at Pierrehumbert's book, p137) we need infrared through ultraviolet.

## Energy balance models at the MAA NCS course on climate modeling

Some quick notes from Esther Widiasih's talk at the MAA North Central Section summer seminar on climate modeling -- thanks again to the MAA and MCRN for sponsoring the workshop!

Start with the Budyko's energy balance model (EBM) -- a linearized version:

$R \frac{dT}{dt} = Q (1-\alpha) - (A+BT)$

with equilibrium solution $T_{eq} = \frac{Q(1-\alpha)-A}{B}.$

This equilibrium is stable with eigenvalue $-B$ (recall $B >0$ ).

What if the earth’s albedo was not $0.3$ ? Remember, albedo of ice is $0.62$ , so changing ratios of ice to land to water change overall albedo.

## Sage worksheet on energy balance model

Attached is a Sage worksheet on the simplest global energy balance model. An energy balance model looks at energy in and energy out:

change in temperature = energy in - energy out

Pretty straightforward, eh? Let $Q$ be the incoming solar radiation (insolation) and $\alpha$ be albedo (percentage of sunlight the earth reflects) -- our "energy in" will be $Q(1-\alpha)$ . Then we can use Boltzmann's black-body radiation to get "energy out" -- it's $\sigma T^4$ , where $T$ is our global average surface temperature in kelvins and $\sigma$ is Boltzmann's constant. So we get the equation

$\frac{dT}{dt} = Q(1-\alpha)-\sigma T^4$

It is not too hard to use calculus to find a linearization near the equilibrium point of this equation and then do some analysis.

The attached worksheet can be loaded into sagenb.org if you want to work through it without installing Sage:

MAA-NCS Climate Modeling -- Boltzmann

I'm trying to figure out how to put up a full interactive worksheet; it's not so hard to put up cells, but I'm not sure about a whole Sage file... let me know if you know!

## Live-ish blogging the MAA NCS Climate Modeling course

The MAA North Central Section is having a summer short course on climate modeling. This morning we've started out with an overview of climate and climate modeling by Samantha Oestreicher. We'll be alternating between lectures and hands-on computer modeling.

I'll be trying to live-blog it, more or less.

Here goes! Some notes from Samantha's talk.

What is climate? Climate versus weather:  "Do I need to own an umbrella?" versus "Do I need an umbrella today?"

How do we observe climate? Data comes from many sources: