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.

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

Wednesday, February 26, 2014

Fish report

One of the highlights of this winter has been my membership in a new seafood co-op.

Each week I go to the farmers’ market to collect my pound of fresh-catch, bring it home, cook it, and feed it to my family. The first week was angel shark, and I gave it my standard fish treatment (recipe below). Next was pacific rockfish, often sold as “pacific red snapper”. This was made into a farmers’ market ceviche, with a variety of market citrus. The third week’s catch was a big hunk of swordfish, which I divided into three steaks, and gave my standard fish treatment with cilantro sauce. Last week was mussels. I sautéed up an onion and head of garlic in half olive oil/half butter while I scrubbed the mussels, and trimmed their beards. Then into the skillet they went along the remaining wine in my glass. I covered the skillet and threw the fresh pasta into a pot of boiling water. I drained the pasta, poured it over the mussels (now perfectly steamed and waiting in their open shells) and mixed in some miso and grated ginger. Delicious.

Recipe: Standard fish treatment for prepared filets or steaks. (oil plus two toppings)

Preheat oven to ~350
Prep fish: pat dry on a towel, salt & pepper, and perhaps a dusting of flour if it’s a thin fish.
Put the fish skillet on the stovetop on a hot flame. 
(I have a few: these are oval-shaped oven-proofed skillets with a handle)
When skillet is hot, add a generous splash of oil and a generous pat of butter.
Plop fish in the skillet. The oil & butter will splatter all over.
Put the oven's top-broiler on.
When fish is halfway done, put on topping 1, and place under the broiler.
When fish is almost done, take out of the broiler & put on topping 2.
Serve in the hot skillet. Fish will finish cooking as you herd your family to the dinner table.

Some of my favorite combinations of oil/topping 1/topping 2
Butter/capers/lemon & parsley
Peanut oil/sesame oil & green onions/lime juice & grated ginger & soy sauce
Ghee/curry & yogurt/cilantro
Olive oil/curry & salsa/parsley
Olive oil/salsa verde/
Olive oil/capers & tomatoes& shallot/parsley & lemon
Butter/shallots/miso & rice wine vinegar

Aqueous reduction reactions

Next in a series of blog posts about one of my favorite subjects, electrochemistry.

The hydrogen evolution reaction is one of the most famous chemical reactions there is. On a water planet like ours, it is the most important reduction reaction.

So, if something is oxidized in water:
            M = M++ + 2e-

Then there are basically only four choices for the reduction reaction.
If oxygen is present, then the reduction reaction is always:
½ O2 +2e- = O-2
In acidic water, the reaction is 2H+ + ½ O2 + 2e- = H2O
In basic water, the reaction is H2O + 1/2O2 +2e- = 2OH-

Note that in acidic water, the reduction reaction of O2 neutralizes the acid.
While in basic water, the reduction of O2 makes it more basic.
Reduction of O2 to O- always moves the pH of the solution up.

But that’s only if oxygen is present.
When oxygen is absent H+ must be reduced in an aqueous system.
This happens at far lower potentials—it takes a lot more energy to make 2H+ take two electrons than  1/2 O2 to take two electrons. (in fact—you can think of oxygen as grabby when it comes to electrons. It’s why breathing feels so good.)

In an acidic environment: 2H+ + 2e- = H2(gas) which bubbles out.
In a basic (or neutral) environment: 2H2O + 2e- = H2 + 2OH

Note—again in both of these reactions, the water evolves to a higher pH—less acidic, more basic.

Questions to consider: Does this mean that the change in pH of the oceans over geologic time is a fundamental marker indicating whether the surface Earth is becoming more or less oxidized?
So: if oceans are increasing in acidity—that means that the Earth is reducing (so ocean rxn is to oxidize). Or if oceans are decreasing in acidity—that means that the earth is oxidizing with time?  

As you consider this question, remember that CO2 is also a big player in the ocean-climate story, adjusting the pH and water chemistry.

In an upcoming post, I examine the hydrogen evolution reactions in some more detail.

Sunday, February 16, 2014

Recent Visit to Mars

I had an opportunity to dig up old data & analysis on the Mars interior for a recent meeting. It was fun on many levels.

First, there’s the fascinating Mars interior with its huge transition zone. Is it drenched with water? Does it show evidence of compositional as well as structural changes? And Mars D double-prime (aka the core-mantle-boundary) is fun to ponder. A single measurement of the core radius will tell us whether there is a transition to perovskite at the bottom of the Martian mantle. A phase transition right at a huge chemical and (likely) thermal boundary layer is interesting—because it will either amplify or dampen instabilities—and therefore help govern dynamics. 

A single data point for the position of the Mars core-mantle boundary will tell us a huge amount about the thermal, mechanical, and chemical history of Mars.

Left: Earth interior density vs. pressure on a log-log scale, so the important parts (for Mars) are emphasized. Right: my preliminary Mars interior density model, based on Earth's, but with 1. low velocity zone removed and 2. increased density of mantle material, due to SNC meteorite constraints suggesting there's more iron in the Mars interior. Depending on the size of the core (which depends on sulfur content to fit mass and moment of inertia constraints), there is either a perovskite layer at the base of the mantle (small, iron-rich core) or not (larger, sulfur-containing core).
 The Mars transition zone is interesting also. On Earth, the transition zone is a relatively small sliver of the mantle, but it's interesting because the steep seismic velocity profile shows that the mineral assemblage is changing throughout this zone. Is it purely a structural evolution (SiO4 tetrahedra to SiO6 octahedra within the garnet) or is it compositional also (e.g. Fe changing? Mg/Si ratio changing?). On Mars, this mineral assemblage makes up the bulk of the lower mantle--and therefore a significant portion of the Mars interior. A measurement of the depth-dependent velocity of the transition zone will also tell us a lot about Earth and Mars.

A mineralogical model of the silicate mantle of the Earth (and Mars).
The minerals that make the transition zone: silicate spinels and garnets happen to be able to store a lot of water in their structures. Up to a percent or so. That's the rock equivalent of a wet sponge. So--if water can get down to the martian mantle, or if it was there and never left, there is the possibility that the Mars interior may store a huge amount of water relative to its surface, and relative to the amount the Earth's interior might store. This could be important for rheology, partial melting, and electrical conductivity. Water softens everything.

Then, there was digging through the old pictures of data collection at the synchrotron. My colleagues Dan and Wendy are there (were they both grad students then?) and a smiling Abby showing off her big baby-bump at the synchrotron. I think I might have been the first pregnant user at the APS, and people wearing ties came to discuss it with me and with the PI of the beamline. See I’m the only one wearing a dosimeter? They checked and rechecked every corner of the hutch with Geiger counters before my time started. I also worked while pregnant at the NSLS. The floor manager met with me before my time and said: it’s safe to go almost everywhere most anytime. Just don’t go near this area during insertion. (I forgot the exact, just remember the gist).

Dan Shim, Wendy Panero, and Abby Kavner  late 1998
The measurement was a high pressure and temperature phase stability and equation of state for FeS, the sulfur-rich endmember of our best guess of Martian core composition—likely along the iron-iron sulfide join. I analyzed the data, developed a model of the Martian interior, and wrote a draft of the paper during maternity while I was nursing my son.

The icing on the cake was that revisiting the science, the data, the history this week coincided with my son’s 15 birthday. So in parallel, I was able to reflect on 15 years as a mom-scientist. He’s thriving as he should, and my mom-heart overflows. My science-heart also pounds, but in different ways than it did 15 years ago. I am still a striver, but my definition of thriving is changing.

It's Alright to Cry

Dear students, colleagues, and others who cry in my office: Not a problem. I’m such a crier myself, I’m almost relieved when you join me. This is a situation I understand. Since my own personal threshold for crying is so low, I never assume that you are necessarily close to or at the end of your tether. Just that you are a person with emotions that you are able to express. I consider myself relatively fluent in the expression of emotions (except anger, which still confounds). Here are some of the emotions that make me cry: Sadness, frustration, anger, Feeling hurt by others, missing someone dear, physical pain, others' illness. Nostalgia. Bad news or sad news. Empathy. Hope Jahren’s blog posts. Crying children. Singing children. Newborn children. Nature. Competence. Good data and/or data analysis. Successful feats of engineering. Art and music.  When I’ve finished the last page of a good book.


Saturday, January 4, 2014

Plate tectonics: 6th-grade curriculum notes

This figure is from a website distributing free science curricula.
http://msnucleus.org/. Coming up with a creative name for an already existing “plate” might be and creative, but it’s not science, and it’s nowhere close to what scientific creativity is like.

I will switcheroo the assignment, also for free.
Here is one way to present plate tectonics to 6th graders, with an emphasis on flexing the scientific creative muscle.
Map 1: Oceans & Continents, showing topography (height)

First look at map 1 (above).  Here is a map of the Earth’s surface showing the topography (height) of the continents and the ocean floor. Find approximately where you live on this map. Is there anything about what you see in the map that leads you to think that the Earth’s surface might consists of rigid crust (plates) that slide around on the surface?  Imagine that the Earth’s surface is divided into about ~12 major rigid plates that slide around on the surface. Based on what you see in the map, try to outline an entire plate.  
Map 2: Earthquake locations for Earthquakes 1963-2008

Now look at map 2: This is a similar map of the surface of the Earth, but the map shows only black or red dots where an earthquake happened between 1963 and 2008. Try to find where you live on this map. Why do you think earthquakes occur mostly along localized zones, and not evenly distributed across the world? Do the localized zones coincide with the boundary between oceans and continental crust? Does the plate outline that you drew on the top map coincide with what you see on the bottom map? Do you think seismologists might have been the scientists who discovered plate tectonics?*

*Hah! That last bit is not for the 6th grade curriculum. That’s just me taking another opportunity to make fun of seismologists!