Back of the envelope (BOTE) calculations are often useful to provide a perspective on the relative importance of a process or system mass balance (inputs vs. outputs). At times BOTE calculations are useful just to give one an idea how to approach a problem and to understand the relationships among the key parameters, and, perhaps, which ones need to be more precisely known. Scientists and others use plots to convey data relationships that are viewed as meaningful—perhaps to examine possible patterns or correlations that can provide insights into cause and effect.
We will use both in this course to help elucidate key ocean system details. So let's practice a bit. The exercise will also let you practice with scientific notation and unit analysis.
Start: A BOTE calculation (it's simple, but let's step through it).
Question: What is the mass of water in Earth's oceans? How would you go about determining this from some basic information? In other words, what values/parameters do you need?
mass [m] is the amount of material that occupies a given volume. We will use SI units, so we'll talk about mass in kilograms (kg).
If you want to write the English sentence, "mass is the amount of material that occupies a given volume" as a math equation, you can write $\text{mass}=\text{volume}*\text{density}\text{}$. Substitute the common symbols for mass, volume, and density, and you can write it as m=Vρ. Density is commonly the Greek lowercase rho.
Let's just check if this makes sense or not: mass is in kilograms (kg), volume is in meters cubed (m^{3}), and density given in mass per volume, or kilograms per meter cubed, kg/m^{3}. So if we substitute the units for the symbols in the m=Vρ equation we get kg = m^{3} * kg/m^{3}. This is good news because some little algebraic manipulation shows we have the same units on both sides of the equals sign.
To obtain the mass of ocean water, we want to know the volume of the ocean and the density of seawater because volume multiplied by density gives us mass. What's the volume of the ocean? We need to find out the area of the ocean and its average depth to calculate its volume. And then we can look up a value for the average density of seawater. These numbers are known reasonably well and we can look them up in any oceanography textbook. Also I trust most internet search engines for "general knowledge" like this, so go ahead.
Note: we will often use several forms of scientific notation: 3.62 x 10^{14,} or 3.62e14 or even 362 x 10^{12}
Area_{ocean}=3.62e14 m^{2} and average depth ~ 3800 m, so (you do the math)...
V_{ocean}=1.375 x 10^{18} m^{3}. Agreed?
The average seawater density is about 1037 kg/m^{3}, therefore we have mass_{seawater}= 1.375e18 m^{3} x 1037 kg/m^{3} =1.426e21 kg. That's about 1.4e18 tons of seawater ( a metric ton=103 kg). Everybody see how we get here (and how to manipulate exponents and units)?
Part 1: A BOTE calculation for you to do.
Part 2: Plotting and Analysis (use your favorite plotting program, but produce an attractive plot with appropriate labeling).
Part 3: Read the postings by other EARTH 540 students. Respond to at least one other posting in each part. You may ask for clarification, ask a follow-up question, expand on what has already been said, etc.
You will be graded on the quality of your participation. This means if you are freaked out by not being able to make a good plot, don't be. Just do your best with that and then focus on doing a good job participating in the discussions. Don't get lost in the weeds here, try to see the big picture. See the grading rubric [4] for additional information.
Links
[1] https://courseware.e-education.psu.edu/courses/earth540/priv/MenardSmithJGR1966.pdf
[2] https://courseware.e-education.psu.edu/courses/earth540/priv/OceanVolume.CharetteSmith.2010.pdf
[3] http://publishing.cdlib.org/ucpressebooks/view?docId=kt167nb66r&chunk.id=0&doc.view=print
[4] https://www.e-education.psu.edu/earth540/grading_rubric_problemsets