# 1.5: Activity 1: Plot, Post, and Discuss

- Page ID
- 14915

## 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 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?

**Digression about mass, density, and volume**

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 mass= volume*density. 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.

**Back to our original problem: mass of the ocean**

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}

**Here are my numbers below, go ahead and look this up if you want to**

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.**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)?*Question:*- 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 depth-range bin) for at least 13 depth bins (Hint: start with 0-200m, 200-1000m, 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(link is external)__This short article may also be of interest__The Volume of Earth’s Ocean, Charette and Smith 2010,(link is external)__ - 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/small-file-size 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(link is external)__. 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?

- 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 depth-range bin) for at least 13 depth bins (Hint: start with 0-200m, 200-1000m, 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:
**Part 3: Read the postings by other EARTH 540 students. Respond to at least one other posting in****each part. You may a****sk for clarification, ask a follow-up question, expand on what has already been said, etc.**