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Making sense of graphs

cuglbl_swht_000.jpg (19218 bytes)
Significant wave heights and wave directions for the N. Pacific.
From the Fleet Numerical Meteorology and Oceanography Center (FNMOC).

Take a few moments to study the image above. What do you see? (Realizing that not everyone has a monitor with great resolution, try to list as much detail as you can.)

You should recognize the continents in brown and the ocean in blue (or similar shades).

You should notice light blue and green splotches of color scattered in various parts of the North Pacific ocean.

You should notice a whole bunch of little arrows pointing in different directions.

If you're really good, you recognized the parallels and meridians. (What are those again? You had better know!)

If you didn't see all of these things, don't despair. That's what this topic is all about.

Graphs, of which the above is one type, convey numerical information in visual form, just like tables. However, they portray data as a picture, in a sense. From the lowly X-Y plot, which we'll review first, to the multi-dimensional 3-D contour plot, graphs display data in the form of a picture.

I quote Douglas A. Segar here (whose oceanography text inspired these sections on maps, tables and graphs): "Graphs are probably the most widely used form of data presentation both in science and elsewhere." Read that last word again: elsewhere. Businesses, especially marketing types, love graphs. They are the ammunition used to engage the mind of the consumer. Properly targeted, a good graph can bring in lots of money. But consumer beware!

While graphs enable us to "see" data and interpret it more quickly than tables, they are not without one major shortcoming. Graphs can lie. Yup. There are no absolute rules for drawing graphs (there are guidelines, however) and graphs can be made to emphasize particular features of data or diminish those features.

Let's take a look at two simple bar graphs (sometimes called charts; technically a chart is a map but that need not concern us here. I will use these terms interchangeably with no distinction between them.)

wpe3.jpg (16307 bytes)

wpe4.jpg (17015 bytes)

Study these two bar graphs for a moment. How are they different? How are they the same?

Both of them have an X-axis (the horizontal axis of a graph) and both of them have a Y-axis (the vertical axis of a graph, for the time being). The numbers that are visually portrayed by the bars the same exact numbers, 130, 133 and 138. Yet the two charts look quite different. Why?

The answer lies in the choice of scales for the Y-axis. Okay, before someone thinks I'm talking about fish or music here, let me provide a definition.

Main Entry: 6scale
Function: noun
Etymology: Middle English, from Late Latin scala ladder, staircase, from Latin scalae, plural, stairs, rungs, ladder; akin to Latin scandere to climb -- more at SCAN
Date: 15th century
1 a obsolete : LADDER b archaic : a means of ascent
2 : a graduated series of musical tones ascending or descending in order of pitch according to a specified scheme of their intervals
3 : something graduated especially when used as a measure or rule: as a : a series of marks or points at known intervals used to measure distances (as the height of the mercury in a thermometer) b : an indication of the relationship between the distances on a map and the corresponding actual distances c : RULER 3
4 a : a graduated series or scheme of rank or order <a scale of taxation> b : MINIMUM WAGE 2
5 a : a proportion between two sets of dimensions (as between those of a drawing and its original) b : a distinctive relative size, extent, or degree <projects done on a large scale>
6 : a graded series of tests or of performances used in rating individual intelligence or achievement
- scale adjective
- to scale : according to the proportions of an established scale of measurement <floor plans drawn to scale>

Wow! What a word. Note that this is the 6th version of the word scale. Definition number three is the closest to what we are looking for. For our purposes (like on a multiple choice test), a scale is a graduated series of marks at specific intervals used to determine some variable quantity (that's my version of it!).

With that definition in mind, what is the scale of the Y-axis in Bar Graph One? What is the scale of the Y-axis in the Bar Graph Two? You should have answered 126-140 for Graph One and 0-140 for the Graph Two (if you answered 150, that's okay too, because technically, the gridline in Graph Two extends to 150).

The choice of scale can dramatically alter our perception of a graph. If the numbers on these graphs represented your scores on three exams and you wanted to show your parents (or anyone that cares) how much you were improving, then you would show them the first graph. If, however, the numbers on these graphs represented your spending habits for three weeks, you would probably want to show your parents (or anyone that cares) the second graph.

The short of it is that the first graph accentuates the differences while the second graph minimizes the differences. Both are perfectly valid graphs, but it is really important to look carefully at the axes (both X and Y) and determine whether what is shown is really a valid interpretation.

I think you get the idea. I suggest that you apply this little bit of knowledge in your daily life, especially when shopping. If you happen to find a particularly good example of "stretching the truth" in graphs, send it along. I'd love to collect some examples and share them with others.

Bar charts are just one type of graph that we will encounter this semester. We will also encounter line graphs (lots of these), pie charts (remember the ocean science budget?), and one of my favorites, contour plots (the image at the top of this page is a contour plot). All of these charts are used to represent data. Some charts work better for some kinds of data than other charts. We won't be so concerned with that here. What I am concerned with is that you know how to read a graph and, to a limited degree, that you know how to plot a graph. That's what we are going to learn next.

Allegedly, the simplest graph is an X-Y line graph (or chart or plot, okay we've introduced a third synonym now). We've already discussed the X and Y axes. An X-Y plot implies by its very nature that there is a cause-and-effect relationship between X and Y. (Steady now, X and Y are just symbols and we already went over that!) In an X-Y plot, X is called the independent variable and Y is called the dependent variable. In other words, Y depends on X.

There are a lot of fancy mathematical ways to express this independent-dependent relationship thing but I have no intention of going there. Rather, let's just review a simple example to make the point. Here it is: Y=5X. That's it. Y equals five time X. In multiplication, it's become more common to leave out the "times" symbol, so when you see two variables or a number and a variable jammed together like that, think multiply.

What this equation means is simple: when X changes, Y changes. If we wanted to reverse their roles, we could write the equation X=5Y. Now who is the dependent variable and who is the independent variable? See how much fun math can be?

Okay, before the math geniuses in the audience start to fall asleep, let me introduce what it is that I really want you to learn this semester. Everybody say hello to the Z-axis. (Hello, Mr. Z.)

Mr. Z really screws with people's minds sometimes (so much that sometimes he's called Evil Mr. Z), but without Mr. Z, oceanography would be even more difficult to understand. The Z-axis represents the third dimension in physical space. (You knew that right.)

Now, here's good pop quiz question: if we represented longitudes (the meridians) on the X-axis and latitudes (the parallels) on the Y-axis (just look at the top image if you're having trouble visualizing this), then what direction could we represent with the Z-axis? I see a lot of head-scratching out there.

If you don't know, then you are still thinking too much like a landlubber, but if you answered "down" (as in depth), then you have proven the strength of your salt.

The Z-axis is used to represent depth in nearly all oceanography graphs you will ever encounter (where depth is an important variable). There's a great reason for it. It's a lot easier to visualize the ocean as a medium from its surface to its bottom. And that's what graphs are all about: visualization.

Let's take a look at a stunning graphic (and JAVA applet) portraying all three axes (x,y, and z). I found this one at Pete Gray's Web Site and you really should do yourself a favor (if you have a JAVA-enabled browser) and go to the web site and play around with the image. You can spin it by dragging it (on the web site, not here) and you can plot a variety of mathematical equations which, even if you have no idea what they mean, look pretty cool in a 3-D graph.

xyz3d.jpg (11346 bytes)

I print-screened this 3-D image from
http://home.echo-on.net/~push/applets/graph/index.html

First of all, note the three axes. In reality, they can be spun in any direction. The important aspect of the three axes is that they remain at 90 degree angles to each other. Note also that the Z-axis is pointed down and the X and Y axes are pointed along the same plane. Although the wire mesh is portrayed along the X-Z plane, it just as easily could have been portrayed along the X-Y plane, in which case it would "appear" like the surface of the ocean.

We aren't going to get into anything this complicated in this course, but I wanted to get you excited about the power of graphs. You can really pack a lot of information into a graph, including 3-dimensional information.

Along with including the Z-axis, oceanographers are quite fond of using more than one X-axis. (Can you tell that oceanographers really go sea hog wild when it comes to graphs?) Here's an example of the kind of graph that we will have to grapple with this semester:

tPNFProfile.jpg (2243 bytes)click here to enlarge vertical profile
Vertical profile of natural fluorescence, PAR and temperature
in the Greenland Sea, August 1998
Source: W. Sean Chamberlin, PhD

Forgive me if this overwhelms your screen, but I wanted this image to be large so you could see the detail.

This plot was generated from data obtained during a vertical profile of the water column in the Greenland Sea with an instrument called a Profiling Natural Fluorometer, or PNF.  A couple terms might be unfamiliar here so let me introduce them now so you have some idea what I'm talking about.

A vertical profile is an up-and-down (from surface to some depth) "outline" or "cross-section" of a particular property of the ocean. Think about a side view of your face. The "line" from your forehead to your chin is a profile of your body, specifically the properties of skin and skeletal structure. Does that help?

We call them "profiles" because, well, they look like a profile and because, scientifically speaking, they represent a vertical slice of the ocean. Functionally, a vertical profile describes how a property changes with depth. Vertical profiles are the bread-and-butter of oceanography and can involve multiple properties and multiple points, as we'll see in a bit.

The term "water column" is another common usage that you need to be familiar with. Although it's more ocean slang than precise terminology, oceanographers sure use it a lot. Simply, the water column is an imaginary column of water from the surface to some depth. The column part makes it more three-dimensional than a profile. Whether it's a cubic column or rectangular column or a fluted Roman Doric column is anyone's guess. The whole idea is to help us think about the ocean's in a three-dimensional way, which, in truth, is a little tough for us two-dimensional terrestrial beings.

So, the vertical profile above displays certain properties of the water column at a specified location (not given) in the Greenland Sea. What do we see?

Shown on the Z-axis is depth, given in meters. You might as well start thinking in meters because that's what scientists use, not to torture students but because it makes life infinitely simpler. A meter is roughly the length of a yardstick, so go with that. What is the scale of depth shown on the plot?

At the bottom of the plot is an X-axis, but it's got a lot of labels underneath it. Those labels refer to the multiple properties shown as lines (and letters) on the profile. Check it out. You should see Ts, Ps and Fs embedded within the lines (actually dots) of the data shown. Those letters identify the particular property to which that line of data displays.

Let's start with T. T stands for temperature. Locate T and Temp on the X-axis. (Hint: they are at the very bottom and although the axis isn't drawn, it is implied. The scale given is to be substituted on the X-axis shown as the bottom line of the square that makes up the entire graph, i.e. where you normally find the X-axis.) You will see some numbers associated with T, namely, on the left side of the Temperature axis, you should see a negative one (-1) and on the right side of the axis, you should see a 29. You should also see a 6.5, a 14 and a 22 deg C, which stands for, you guessed it, 22 degrees Centigrade.

Take a moment and look at the temperature data plotted on this graph. At what depth(s) do you find the warmest temperature? At what depth(s) do you find the coldest temperature?

Shezzbad, you can't figure out the depths? You see the line for temperature but don't understand it? That's okay. Take a look at the left hand side of the graph, what we have identified already as the Z-axis, which we have said refers to depth. You see the numbers 0 and 52 right. Along the vertical line between those numbers you should see a bunch of little tick marks (look for short lines, not gross little insects!). On the graph, there are actually two sizes of tick marks, large and small, if you look really carefully. Each tick mark represents an interval of depth. What is the interval of depth between each large tick mark? between each small tick mark? Click here to check your answers.

What you should notice about temperature in this graph is that it is the same from 0 meters down to approximately 12 meters, where it decreases sharply for a meter, levels off for one meter (at about 15 meters) and then decreases very rapidly until about 18-20 meters where it decreases more slowly until about 35 meters where it starts to increase slowly again. Trace the line with your pencil (or something that won't smudge your screen) and follow it from the surface (0 meters) down to 52 meters, where the vertical profile stops. (It stops there because that's as far as I lowered the instrument, not because it hit bottom.)

How do you figure out the temperatures? Take a look at the vertical lines that are drawn across face of the graph. One vertical line is placed at about 6.5, another at 14 and another at 22. Can you see that? Those are the tick marks for temperature on its X-axis (which is a linear axis, i.e. there are equal intervals between the tick marks). You should be able to clearly see that the water temperatures in this graph are all below 6.5 degrees. To figure out the exact temperature at any particular depth in this graph, you could use a ruler to determine the exact distance between -1 and 6.5, divide that distance into equal intervals and assign temperatures. Don't worry if you don't understand that completely right now.

Take a look at the other two X-axes, the ones for P and F. P stands for Photosynthetically Available Radiation, or PAR, which is not a golf term but a term used to describe the colors of sunlight that are visible to us and plants. (Technically, they are the wavelengths of light (which is what makes different colors) between 400 and 700 nanometers. These wavelengths are the wavelengths of sunlight that plants use to make sugars, i.e. to photosynthesize. This is my favorite subject and we'll get to it in another lecture.) F stands for Fluorescence, which, in this case, is the natural fluorescence or red light that is emitted by plants during the process of photosynthesis. You don't need to understand this material just yet. It's my area of research and you will be illuminated on it later.

Follow the lines (and symbols) for P and F. P decreases pretty much as a straight line from the surface to 52 meters. F decreases rapidly at the surface, then more steadily until just below 30 meters, where it takes a jump. Below that, F decreases pretty quickly. That bump at 30-32 meters is where all the phytoplankton are living. Phytoplankton are the single-celled, microscopic plants that drift in the ocean, provide half of the oxygen that we breathe and upon which most organisms in the ocean depend for food. Hint: They are way important. Learn how to pronounce that word: fi-toe-plank-ton. Commit it to memory. What are they? Single-celled plant drifters. Got that?

Now take a look at the X-axes for P and F, again at the bottom of the graph. P is given as wPAR (or water PAR, meaning light in the water) and F is given as LuChl, which I won't even go into at this point. (I don't want you to collapse from terminology overload just yet.). The scale for P ranges from 1 to 10k, which is the equivalent of 10,000. The scale for F ranges from 0.1 to 1000 (1k). The units are also listed but don't be concerned with their meaning.

Note the tick marks on the X-axis for these properties, which is the horizontal line that forms the bottom of the square of the plot (in other words, it's where we usually find X-axes). What are they doing? They are not spaced at equal intervals like the Z-axis. They bunch up right before each vertical line, then spread out and bunch up again. What gives?

As we will discuss in another lecture, P and F decrease in an exponential fashion as a function of depth in the water column. No, you don't have to know that yet. What it means is that these two properties are not linear. They don't behave like a straight line. They are what we call non-linear. Don't worry about these terms. We're not about to go into non-linear math in this course. I just want to expose you to the concept, so that if you do want to know more or have some background in non-linear functions, then you'll have some idea what I mean.

I'm sure that all of you at some point in K-12 heard about logarithms or log plots (and I'm not talking about the kind of logs treasured by Log Lady on Twin Peaks, either). You probably forgot about them or didn't understand them or didn't want to understand them. That's the way I felt about them until I started working with them in graduate school. Anyway, the X-axis in the above plot that corresponds to P and F is a log scale. That's all you need to know. I won't ask you to read a plot with a log scale, but I thought you should know what it looks like anyway.

Looking at all the paragraphs I have written from the bottom of the above vertical profile to this point should give you some idea for the incredible amount of information that is contained in one simple graph. I mean, really, there's a lot going on in that figure, and we have barely scratched the surface with it. We will spend many more pages together (perhaps hundreds of pages) to develop a complete understanding of that one simple graph. Awesome, isn't it?

Before we leave simple X-Y-Z plots, I want to tell you a little about the PNF. It is a simple profiling instrument that can be lowered by hand from a pier or a small boat. It has sensors for temperature, pressure (depth), PAR and LuChl (or natural fluorescence). Electronic signals from the sensors are transmitted from the instrument through a waterproof cable (called a sea cable) to a deck box (packed with electronics) that converts the signals to digital information that is sent to a computer (usually a laptop) where the data are stored and displayed. The graph shown above was obtained in exactly this fashion.

We are highly fortunate at Fullerton College to own such an instrument. Thanks to the Natural Science Budget Committee, we were able to purchase a PNF in summer 1999. With the acquisition of a new vessel in summer 1998, a 21-foot fiberglass boat called the Que Mas, we have quite the powerful tools for teaching students about oceanography. These tools allow students in field labs to practice and experience the same techniques used by oceanographers in any ocean in the world. The PNF used to obtain the above profile aboard a 211-foot research vessel (the R/V Johan Hjort) in the Greenland Sea is the same type of instrument we use in our oceanography labs. The only difference is that there are no icebergs to watch out for in southern California!

Now that you are starting to get the hang of reading graphs and starting to get some feeling for the level of attention to detail that is required, let's take a look at one more type of graph that is widely used to give oceanographers a sense of what is going on in the ocean. This particular type of graph is called the contour plot (or graph or map or whatever).

Contour plots, of which there are many forms, portray 3-D data in a kind of 2-D way. Let me start with an example.

Say you wanted to take a hike to the top of a mountain. Before your hike, you purchase a map because it's always a good idea to have map. Besides that, you want to plan the route that avoids the steepest parts of the mountain. You open the map and take a look at it. How does the map provide information about elevation?

The map uses something called contour lines. Say what?

Try this little exercise. Make a fist with your hand. Imagine that your knuckles are a range of mountains, call it the five sisters or five brothers, whatever. Take a pen (felt pens work best) and trace a couple lines of equal elevation around one of your knuckles. In other words, draw a circle around the base of your knuckle, then halfway up the knuckle, then a small circle around the very tip of the knuckle. If your knuckle were a mountain, the circle that you have drawn would represent everywhere on that mountain that was the same height above sea level (i.e. its elevation). Now, flatten out your hand (quit making a fist). What happened to the lines of elevation? Are some parts of the circles closer together than other parts of the circles?

What you have done is taken 3-dimensional information and turned it into 2-dimensional information. If you had labeled each circle as a particular height along your knuckle (the base might be zero and the top of your knuckle might be a half inch), then you even read the elevations along your knuckle. It should be apparent that places where the circles are closer together are going to be steep, in other words, elevation changes rapidly. In areas where the circles are further apart, the elevation changes are going to be more gradual.

Contour plots that are used to display changes in elevation on land are called topographic maps and no sane hiker (or mountain biker) would be without one. Here's one for Mount Rainier, in the state of Washington, courtesy of the United States Geological Survey (USGS) page on Finding Your Way with Map and Compass.

trainiertopo.gif (5036 bytes) click here to enlarge Mount Rainer topo map

Note the ridge that extends from the bottom right-hand corner of the map. You can also see that areas right at the top are more flat (where contour lines are further apart) than areas on your way to the top. Of course, I expect all of you to end up at Point Success, which is where all good oceanography students strive to be.

Contour plots can be used to portray just about any kind of 3-dimensional information, not just elevation. Ocean geologists (and lots of people in the shipping and boating business) make use of contour plots to illustrate bottom depths in different regions of the ocean. These type of contour plots are called bathymetric charts or maps. For waterways used in recreational and commercial boating, NOAA publishes nautical charts that depict bottom depths, among other important navigational features. For scientific purposes, the USGS conducts regular surveys. Other agencies are also involved in these important surveys.

Here's an example of a bathymetric chart for the Monterey Bay submarine canyon, which is larger than the Grand Canyon :

tmbay_map.gif (2603 bytes)click to enlarge Monterey Bay bathymetric map

Check out the spacing between the contours, which gives you an indication of how steeply the canyon drops off. It gets deep quite near to shore where the mouth of the canyon approaches Moss Landing. (See where the gray lines come to a point at the right of the image? That's Moss Landing.) Note also the contour interval of 50 meters. That means that each line from shore to sea is 50 meters deeper; that is, there is a 50 meter (~150 feet) difference in depth between each contour interval. The deepest place contour labeled on this map is 2000 meters, more than a mile deep!

I'm going to jump ahead here for a moment because bathymetric maps in the modern age can get quite spectacular. Here's another view of the Monterey Bay submarine canyon with a little 3-D imaging thrown in. The bathymetric data are the same, but the type of contouring is, as you can see, quite a bit different.

t3dmonterey.gif (10993 bytes)click to enlarge Monterey Bay 3-D bathymetry

Pretty bitchin', huh? Note that instead of contour lines, colors are used. Each color represents a particular depth interval. See that band of colors at that bottom of the image? That's a color key. What is the scale for the color key? Take a look at both ends: the left end (the blue end) has a value of -4000 meters. At the right end (the red end), the scale reads +1400 meters. Now in this map (I guess because geologists made it), negative values refer to vertical distances below sea level and positive values refer to elevations above sea level. Just remember that oceanographers typically consider the Z-axis (i.e. the depth axis) to be positive downwards (so that oceanographers refer to depth as 30 meters in water that is 30 meters deep). While this may see confusing, it really doesn't matter as long as you look at the key and read the scale. In this image, blue values represent ocean bottom features while red values represent landforms.

All this talk about scales makes this an ideal spot to introduce a general discussion for scales that we encounter in the ocean, namely, spatial scales and temporal scales.

I think we could all agree that the oceans cover quite a bit of territory on our planet. Properties of the ocean, such as water temperature or salinity (the concentration of salt in the ocean), can vary quite a bit from one end of the ocean to the next and from the top to the bottom as well. Ever dove into a lake in summer and found it quite cold beneath that warm surface layer? Then you know what I mean. Simply put, ocean properties change with latitude and longitude and depth.

Another way to say this is that ocean properties change across spatial scales. What are spatial scales? Think about what defines a physical space, like your bedroom or a chunk of ocean. Your bedroom has a length and a width and a height; the ocean has latitude, longitude and a depth. Same thing. We've already discussed a scale as an interval of some property. Given all that, what are the possible spatial scales in the ocean? In other words, what are the possible intervals of space in the ocean? Think of the smallest distance you can imagine and think of the greatest distance you can imagine and figure out where the ocean fits between those two distances. Click here to check your answer. If you don't understand this, e-mail me or post a message. It is fundamentally important.

In a similar but slightly more abstract fashion, the ocean changes over temporal scales. Temporal simply means time or having to do with time. Thinking again...what are the smallest scales of time you can think of and what are the largest scales of time you can think of? What are the temporal scales of variability in the ocean (great quiz question!)? Click here to check your answer. E-mail me or post to the forum if you don't get it.

These spatial scales (and temporal scales, too) lend themselves well to contour mapping. Contour maps let us take a slice out of the ocean like a page out of the phone book. When we stack these slices together, we can visualize the entire ocean.

The image at the top of this page is a good example of using a contour map to show how features change over the surface of the ocean. The spatial scales here are latitude and longitude. These are two of the dimensions portrayed. The third dimension (although it is not a spatial scale) is wave height. The patches of color you see refer to the heights of waves; the green colors are the highest waves. This contour map also portrays a fourth dimension, the direction of the waves. Thus, in a flat, 2-D image (your screen), we can visualize 4-dimensions of information: latitude, longitude, wave height and wave direction.

Don't be confused by the word dimension. A dimension doesn't have to be physical dimension, like length, width and depth. A dimension can be a property, like temperature, salinity, wave height or wave direction, and this is the sense in which the word dimension is used most often in oceanography.

As a final example of contour maps, I want to take you to the Greenland Sea again to demonstrate the power of contour maps for understanding ocean properties. Let's first start with a map of the cruise tracks for our expedition. Cruise tracks are the road, so to speak, over which the ship sail while at sea.

tcruisetracks.gif (2787 bytes)click to enlarge the Greenland Sea

The cruise tracks in this particular image are represented by blue dots, which, in fact, are the location of sampling stations. (Technically, the cruise tracks would be the line that we draw from dot-to-dot, since the ship must travel over the ocean to get to those points. The cruise tracks are not shown here.)  The dots indicate places where major oceanographic sampling was performed, typically over a period of 24 hours. These are what we call Big Stations. One other feature of this map I would like you to notice are the colors. Obviously, land is brown, but can you see the shades of light blue, blue and purple? The purple areas are the deepest. These deeper regions are known as basins (just like a wash basin!) The basin over which the station dots are located is the Greenland Sea basin.

Between Big Stations, profiles of ocean properties were obtained using a CTD, the acronym for an oceanographic profiling instrument that measures conductivity (which translates into salinity), temperature and depth. Only the most easily measured ocean properties were obtained at these stations, which we call Little Stations.

To make a contour plot, we need a minimum of three dimensions. Let's take a look at one section along our transect (another word for cruise tracks) and see what profiles of temperature look like.

tcutgrnseaxsec.gif (2082 bytes)click here to enlarge section of Greenland Sea transect

On the right hand side of this figure, you should recognize a vertical profile (an X-Z graph), very similar to the one we studied above. On the left hand side, you should see a zoom-in of the Greenland Sea basin over which the station dots for all the Little Stations are placed. The vertical profile is a composite of temperature measurements that were made from the surface to the bottom depth along one section (east to west). In other words, pick a set of dots in a line from right to left and that's a section. Put all of the vertical profiles of temperature from each one of those dots on one X-Z plot and you've got the graph on the right hand side of this figure.

Let's review a moment. Between these two figures, the map and the vertical profile, we have information on latitude, longitude, temperature and depth. But we have eliminated latitude in the vertical profile: the stations at which these profiles were performed all occur at the same latitude. (Can you see that? We've chosen an east-west section so that we don't have to worry about changes from north to south.)

So we now have longitude, depth and water temperature. Let's make a contour map:

tcutoutxsec.gif (2698 bytes)click here to enlarge temperature cross section in the Greenland Sea Basin

This contour map, sometimes called a cross-section, shows the distribution of temperature from the surface to the bottom along one section from east to west in the Greenland Sea. Take a couple minutes and study it. What do you see? Colors? Good. A color key? Even better. Look at the key. The blue colors represent cold temperatures and the green, yellow and orange colors represent warmer temperatures. Where is it coldest on this contour map? Where is it warmest? Click here to check your answers.

Now, we have to play some mind-visualization games, but they should be fun and instructive. Look at the contour map. Imagine a little ship traveling from right to left along the top edge of the contour map. Every so often, the ship stops, lowers an instrument, a CTD, from the surface all the way to the bottom. See the black color at the bottom of the contour map? That's the sea bottom. The ship raises the CTD and motors on its way a little more. It stops and repeats the procedure, collecting vertical profiles all along the way until it gets to the east side (the left hand side of the contour map).

The vertical profiles your little ship just made are the same exact vertical profiles shown in the figure above. Each temperature profile was taken at a Little Station and this information was used to construct the contour map.

Try this one: Look at the vertical profile graph more closely. Can you see that some profiles start out warm at the surface and get colder? Can you see that some of the profiles start out cold and get warmer? If you were on your imaginary ship, which vertical profiles of temperature would correspond to locations on the eastern side (right-hand side) of the contour map? Which vertical profiles would correspond to locations on the western side (left-hand side) of the contour map?

It should make sense to you that the vertical profiles that start out colder and get warmer are the vertical profiles represented on the left-hand side of the contour plot. Trace your finger in a vertical direction along the left-hand side of the contour plot? How do the colors change? They go from blue to lighter blue to green to light blue again. If you look closely, you can see the same exact trend in the vertical profile. Try it with the right-hand side of the contour map.

One more imaginary visual: Look at the station map above and then look at the contour map. Try to imagine the contour map as a thin slice of the ocean (like a page in a book) whose top edge lines up with the east-west station dots (one section) and whose bottom edge rests at the bottom. Because we have a bird's-eye view of the station map, we are actually looking down on the surface of the ocean. The contour map is a thin slice heading into our computer screen. What if we rotate the station map so that it represents the surface of the ocean as we know it? In other words, imagine that the station map is a piece of paper and rotate it so that the "paper" is horizontal or flat. Then place this piece of paper (the station map) on top of the other piece of paper (the contour map) and line them up where we took the section.

If you are really struggling with this, take some colored pens or crayons and duplicate the station map and contour map. It doesn't have to be a perfect representation, just so you have the general information. Then rotate the pieces of paper and see how the contour map is a vertical slice of the station map. The two pieces of paper will make a "T" if you do it right.

No doubt your head is swimming by now, so let me tell you a story from my youth. When I was a wee lad of 6 or 7 years, my mom took my sister, brother and me to swimming lessons. We lived in Florida and she wanted to make sure that if we ever fell into an alligator-infested lake that we knew how to swim. Our swimming instructor, Mr. Ritz, wore a helmet, like one of those safari helmets. With all the kids gathered around the pool, he would throw his helmet out into the middle, then dive in and come up under it. He always came up with the helmet perfectly placed on his head and of course, all us kids laughed and clapped. He was such a nice man...underwater. But once he came up under that helmet, all hell broke loose. He started screaming and yelling and threatening to throw kids in the water if we didn't jump right in and start our lessons. Anybody afraid of the water was done for. It was sink or swim in his class. The way he figured it, he would rather have us kids be more afraid of him than the water because knowing how to swim could save our lives. I guess it worked because I learned how to swim, but it was a heck of a way to learn something.

While many of you may feel after reading this particular lecture that you have been thrown into the water and told to start swimming, let me assure you that I am no Mr. Ritz. If this material has just overwhelmed you, don't be afraid. It was designed to throw you into the ocean feet-first, but not to drown you and definitely not to make you afraid of the water. The intention here is to broaden your perspective and give you a taste of what's ahead. Your main focus should be on learning how to read graphs, not to know how to interpret or understand the processes they represent. It's way to early for that!

This lecture on graphs has introduced a lot of new concepts. It has asked you to visualize information that is perhaps totally unfamiliar to you. You have been asked to examine closely many fine details. If you didn't get it all at first, that's okay. Let these waves of information wash over you. Go back through the general ideas and practice. Practice reading graphs and maps and practice explaining what they represent.

Making sense of graphs is one of the most valuable tools you can ever develop, no matter what career you plan to pursue. Please e-mail me or set up an appointment with me in my office if this material has gone completely over your head. I'd be happy to pull out some of my maps and graphs and help you explore the fascinating world they represent.

For more fun with oceanography graphs, check out these web sites. You'll be amazed at how beautiful a graph can be, even if you haven't the foggiest what it means. The NOAA site even has an animation of El Nino/La Nina, which combines spatial and temporal scales into one image.

Surf long and prosper!

El Nino/La Nina animation from Climate Diagnostics Center at NOAA
http://www.cdc.noaa.gov/

The Tropical Atmosphere Ocean Array - Lots of visualizations of sea-surface temperature data
http://www.pmel.noaa.gov/toga-tao/

Answers:

A. each large tick mark (_) represents 10 meters while the small tick marks (-) between them represent 5 meters. Count down the tick marks and verify it for yourself if you didn't get it right.

B. Spatial scales in the ocean include distances as small as molecules (nanometers, 10^-9 meters) and as large as miles (thousands of miles, in fact).

C. Temporal scales in the ocean range from femtoseconds (10^-15 seconds) to millennia (thousands of years, in fact).

D. The coldest temperatures (in blue) are at the surface on the western (left-hand) side of the section. The warmest temperatures (in yellow) are just below or at the surface on the eastern (right-hand) side of the section.

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