Activity 1: Quantitation and Plot Analysis (1)
Directions
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 give us an idea of your facility 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, units in kilograms (kg) SI system); and $\text{mass(m)}=\text{volume(V)}\times \text{density(}\rho \text{)}$ , where density (rho) is the mass/unit volume (depends on the substance), given in kg/m^3.
V=length(l ) x width(w) x height(h) (or depth(d)), or, because Area(A)=l x w, V(m^3)=A (m^2) x d(m).
To obtain the mass of ocean water, we would need the area of the ocean and it's average depth to calculate the volume of water, and a value for the average density of seawater. These numbers are known reasonably well and we can look them up in any oceanography textbook.
Note: we will often use several forms of scientific notation: 3.62 x 10^{14,} or 3.62e14 or even 362 x 10^12
A=3.62e14 m^2 (from 3.62 x 10^8 km^2) and d(avg)=ca. 3800 m, so (you do the math)...
Vocean=1.375 x 10^18 m^3. Agreed?
The average seawater density is ca. 1037 kg/m3, therefore we have mass_seawater= 1.375e18 m^3 x 1037 kg/m^3 =1.426e21 kg. That's ca. 1.4e18 t 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.
 Question: What is the mass of water in Earth's interior? How would you estimate this? What values would you need (there might be several ways to do this)?
 Give it a try and post your answer in the "Lesson 1, Activity 1" discussion forum in Canvas. Engage your classmates in discussing final calculations and critical values.

Part 2: Plotting and Analysis (use your favorite plotting program, but produce an attractive plot with appropriate labeling).
 Find data (on the Web or in an oceanographic textbook, provide source) for the proportional distribution of water depths (area of the seafloor in each depthrange bin) for at least 13 depth bins (Hint: start with 0200m, 2001000m, then intervals of 1000m to maximum depth of the ocean). This may be hard to find. If you run into trouble you can use this source: Hypsometry of Ocean Basin Provinces, Menard and Smith, 1966 This short article may also be of interest The Volume of Earth’s Ocean, Charette and Smith 2010,
 Plot the distribution of depths as a function of the percentage of total ocean area (must sum to 100% of course). You now have what is termed a hypsometric curve for the oceans. Post this plot in the "Lesson 1, Activity 1" discussion forum in Canvas. You must figure out how to attach your plot in your post. I would suggest that you first save it as .jpg or .png or some other simple/smallfilesize format. Make sure that your plot is high quality: both axes should have clear labels with units and the lines/symbols should be clear. For example, look at the plot on page 19 on this article, The Oceans, Their Physics, Chemistry, and General Biology. It's a great example.
 Discuss how such a curve could provide insights into how the ocean basins formed. Why are some depth intervals such a large proportion of the ocean area? How else might a hypsometric curve be useful?

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 followup question, expand on what has already been said, etc.
Submitting your work
 Enter the "Lesson 1, Activity 1" discussion forum in Canvas
 Create a new post for each of parts 1 and 2 and then, in separate posts, create one or more replies for part 3
Grading criteria
You will be graded on the quality of your participation. See the grading rubric for additional information.