Tuesday, March 18, 2014

Fermi Problems and Earth's Surface Heat Flux from Interior


One of the things I teach in my undergraduate courses is how to do order-of-magnitude calculations.

An order-of-magnitude calculation (otherwise known as “Fermi-problem”) is a method to estimate quantitative answers for complex problems by combining smart logic with pre-calculus arithmetic. No calculators allowed! But scrwaling on napkins is encouraged.

Here’s one of my favorite order of magnitude questions because 1. It’s not difficult 2. But it’s an interesting Earth problem 3. With gobs of science-y richness at its center. I do it in all of my undergraduate and graduate geophysics classes.

The problem is this: Given the following map of surface heat flux, make an order-of-magnitude of the total surface heat flux coming from the Earth’s interior.


Map of Earth's Surface Heat Flux From Davies and Davies (2010) via Wikipedia
Here’s how I break it down for an undergraduate class:

1. What quantity is mapped here and what are the units?
2. What are the lowest values and where are they?
3. What are the highest values and where are they?
4. What is the average value of heat flux for the surface of the Earth?
5a. optional—how does this value compare with an incandescent light bulb (I can joke here about how this question will be obsolete soon)
5b. optional—how does this value compare with our own (human) energy output? (appeal to the ergometers machine at the gym here)
5c. optional—how does this value compare with the solar heat flux?
6. Now that we have an average value for heat flux, what other information do we need to get the total heat?
7.  How does one estimate Earth’s surface area? (crowd-source for formula for surface area of sphere –remind students that this is a good formula to memorize. Crowd-source for Earth’s radius of Earth. Encourage students to use iphones/internst for this step.)
8. Pretend that students are already perfectly competent to calculate order of magnitude surface areas once they have the values of radii and formula. Suggest that they round up to 1 sig digit on the radius and suggest that 4 * pi =10.
9. Then remind students to deal with units.
10. remind students that numbers with 10^12 have prefix “Tera”
11. Students should get an answer that is roughly 50 terawatts.
12. Watch them smile when they realize that the five or ten minutes that we have spent on this problem gets them fairly close to “accepted” values ranging from 44 to 47 TW.

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Next up—where the map above comes from, another teaching opportunity for the concept of diffusion, why the total heat flux is important, and how and why scientists argue about it.  


Saturday, March 15, 2014

Fish report 2: Abby vs. Anchovies!


Recently, one of our department visitors (prospective grad student? Faculty candidate? One of the plate tectonics undergrads during office hours?) surprised me by asking me what my hobbies are.  I hadn’t thought about “hobbies” per se in so long that I needed to reframe the question for myself in order to answer it:

What, outside work and family, enriches my life?
(note—this is different from wikipedia’s defn. of hobby as something done regularly for pleasure, usually during leisure time.)

Well there’s food. I hesitate because I don’t want to erode my efforts to patiently educate my family to Never Call My Cooking a Hobby! The education consists of the following proclamations spoken as loudly as possible, while swinging around and pointing my kitchen knife directly at my students: What??!!? You classify the work that I do to prepare good food for the family as a hobby? Just because I get joy out of doing this job does not devalue the fact that it is still labor!! My Labor!!! (If my son is getting the lecture I might go off on a tangent about the labor involved bringing him into the world...) The lecture material is even more effective when I’m in the midst of preparing animal carcasses. Then I hand out assignments to whatever pupils might still be nearby: Taste the sauce & tell me what it needs! Chop the onions! Take out the garbage! Pour me a drink!

Recently, Santa Barbara’s Community Seafood Cooperative expanded and the past two months I have had my seafood share delivered to Santa Monica’s wonderful Wednesday produce market. I already wrote about the first month: angel shark, rockfish, swordfish, and mussel

Now I’m noticing I haven’t blogged since last month’s fish report. It’s not that my work/science/professional life doesn’t offer untold richness in potential blog material. I’m working on revising a paper for resubmission, and will blog about that science. I will blog more thoughts on how academia and academics, science and scientists, all suffer from lack of diversity. But while I was juggling big loads of teaching, research and service this past quarter, it has been much easier just to blog about seafood, if at all.

This past month dealt some difficult shares. First, windy weather and storms cancelled the share delivery. We mused about familiar themes of man-versus-nature over take-out pizza.  The next week there was a big pile of ridgeback shrimps, who looked remarkably alive as I twisted off their heads and removed their exoskeleton and had them sit like maggots in the colander. Squeamish? Sorry. Can’t be squeamish about the food share. Plus they fight back—at the end of the process my hands were red & swollen from tiny shell-shard cuts. They were delicious sautéed pink with lots of shallots and butter and eaten with linguine.

Week 9 of any academic quarter is never a high point. There are hardworking and tired grad students, lab work, proposals due, late reviews, cranky colleagues, faculty interviews, dog-and pony show for hordes of prospective graduate students, papers to write, lectures to give, plus it was my week tweeting as one of the @realscientists. In short: total spread thinnage and academic exhaustion at work while at home a second full week of single mom-dom due to traveling spouse. And in the middle of the week, I squeeze time to run to the market to grab my seafood share: a generous pound of small, still shimmering anchovies, and they’re looking at me with all their shiny eyes and I’m looking at them saying Fuck You, Anchovies Because You Are Not Arriving at a Time in My Life When I Can Deal With You. Into the freezer they went.

The weekend came and I slept and spent time with family and friends and rested. By Sunday afternoon I was ready to face down the anchovies. I defrosted them under running water. Between anchovy #5 and #10 I got the hang out of cutting off the head, finding the correct ventral cut, pulling out the guts, and then zipping out the backbone. I layered them in a ceramic bowl in piles of salt. I filled the bowl to the top with vinegar (sherry plus apple) and threw them in the fridge. I woke (too) early Monday morning, rinsed off the salt & vinegar & layered them in good olive oil & parsley & garlic & went back to sleep. Monday night they were cured.

This batch was too salty for eating on their own (next time—shorter salt marinade: 2-3 hrs instead of 12…) But they are perfect ground into pasta sauce ( one or two anchovies sautéed with the garlic & onion & tomatoes & red pepper over pasta) and Caesar salad dressing  (two anchovies blended with lots of parsley, more olive oil, meyer lemon juice and a barely poached egg & poured over salad). And they were great as the sauce on last week’s share: swordfish.

Anchovies in their salting phase