1.4: How to Study Ocean Data

Before we begin to explore the intricacies of the relationships among humans, the oceans, and the environment, it is important to review some of the basic tools used to describe the Earth and its oceans. These include various forms of maps, graphical representations of data that vary geographically or with time, graphs that can show the relationship between two variables, and standard scientific notation for numbers and units of measurement.

As is true for other sciences, describing what we know about the oceans and ocean processes requires the use of graphs and similar diagrams, and sometimes mathematics. For ocean sciences, we must also be able to represent data in a geographic context, which requires the use of maps or charts. Graphs, diagrams, and maps make it easy to understand certain features of even complex data sets without using mathematics (a goal we have set for this text). However, these visual representations can be properly interpreted only if we understand how a particular graph or map presents, and often distorts, the data. To make it possible for you to properly study and understand the rest of this text, the remainder of this chapter discusses some of the characteristics of graphs and maps that are used extensively in this text. Even if you are familiar with scientific diagrams, you are strongly urged to review this material.

Graphs

Graphs are probably the most widely used way to present data in science and elsewhere. They provide a means of visualizing relationships between two or more variables or properties, but they can be extremely misleading unless they are read properly. To understand a graph, you must not only look at the general shape of the line or curve connecting points or the apparent difference in sizes of bars in a bar graph, for example, but you must also carefully examine the axes. Two simple examples in Figure 1-5 illustrate why.

In Figure 1-5, three simple values that could be, for example, the prices of an item at different stores or the depths of the thermocline at three locations in the ocean are plotted in a simple bar graph. The same data are plotted in both parts of the figure. Why do the plots look so different? In Figure 1-5a, the y-axis (vertical axis) extends from 0 to 250. In Figure 1-5b, the data are “expanded” by showing only 228 to 240 on the y-axis. Items 1, 2, and 3 have nearly the same values, but one plot seems to show that item 3 has a much higher value than items 1 and 2. Have you ever seen this technique used in advertisements or news reports to present data differences in a misleading way?

Figure 1-5. Two bar graphs that show the same data but use different y-axis ranges. They give very different impressions about the differences among the three values. In part (b), the true nature of the differences can be found only by carefully examining the scale on which the data is plotted.

 

The second example is a simple nonlinear (CC10) relationship between two variables (x²= y). These variables could be, for example, light intensity and depth, or primary production rate and nutrient concentrations (although the relationships between these pairs of parameters are actually more complicated). Notice that the first plot (Fig. 1-6a) shows that y increases more rapidly as x increases, which is exactly what we would expect from the equation. However, the same data in Figure 1-6b appear to show the exact opposite (y increases more slowly as x increases). The reason for this difference is that the y-values are plotted as the log of the value, not the value itself. Log plots are commonly used for scientific data but may be confusing unless you examine the axes carefully. One of the reasons why log plots are used is illustrated in Figure 1-6c. This figure is a plot of the same data as in Figure 1-6a and Figure 1-6b, but it plots the log value for both variables. The plot is a straight line, revealing a feature of this nonlinear relationship that is often important to scientists.

Figure 1-6. A simple nonlinear relationship is plotted in three different ways to show how logarithmic scales can change the apparent nature of the relationship between the two variables: (a) a linear–linear plot, (b) a log–linear plot, (c) a log–log plot. Notice that in parts (b) and (c), the scale on the log axis can be expressed as the log of the number (left side) or the number on a log scale (right side). This shows how important it is to analyze every part of a figure to distinguish the details like those seen in Figure 1-6.

Contour Plots and Profiles

Contour plots are used to display the two-dimensional spatial distribution of a variable, such as atmospheric pressure on weather maps. The variable plotted can be any parameter, such as pressure, temperature, soil moisture, vegetation type, or concentration of a substance.

Contour plots show how variables are distributed across flat surfaces. In some cases, the variable being plotted represents a measurement in the third dimension—perpendicular to the surface—such as depth or height. The most common examples are topographic maps that depict the height of the land surface above sea level and bathymetric maps that depict the depth of the ocean below sea level. Sea level is used as the surface on which the third dimension variable, the height or depth, is plotted. Contours of pressure are usually called isobars, temperature contours are isotherms, density contours are isopycnals, and depth contours are called isobaths. The prefix “iso” means “equal” or “the same,” so these lines connect locations with the same value of the variable, with each line representing a different value. Often, but not always, the values contoured are spaced at equal intervals of the variable, such as 50 m, 100 m, 150 m, and 200 m above sea level for a topographic map. One very important rule of contouring is that contours cannot cross or merge with each other. This is because each contour line always follows its own value. If the plotted parameter is elevated or depressed (forming hills or depressions) in two or more areas, contours around any two such features do not connect with each other. Instead, they form closed loops unless they are at the edge of the plot (Fig. 1-7). Contour lines show the distribution and magnitude of highs and lows of the plotted parameter. In any particular contour plot, high and low features (hills and valleys in a topographic map) that have more contours surrounding them are of greater magnitude than those with fewer surrounding contours. For example, higher hills are shown with more contour lines between sea level and the summit than lower hills. Contours also reveal the strength of gradients at different points on the plotted surface. Where the contours are closely bunched together, the value of the parameter changes quickly with distance across the surface, and the gradient is relatively strong (steep terrain on a topographic map). Conversely, where the contours are further apart, the gradient is relatively weak. The term relatively is important because the number of contours and the intervals between the contours can be different in different plots; even plots of the same data, which can be seen by comparing Figure 1-7a and Figure 1-7b.

 

Figure 1-7. Contour plots. These plots reveal areas of higher and lower values of the plotted parameter, identified as H and L. They also indicate the strength of the gradient, which is stronger where adjacent contours are closer to each other. (a) In this example, which is a topographic map of the seafloor, there is a flat plateau at point A, a steep-sided valley at point B, an area of gentle slope at point C, a depression at point D, and a hill or mountain at point E, which has a very steep slope, especially on its right side. (b) Here, the same data are plotted with a greater interval between contours. Unless you examine it carefully, this plot can give the appearance that gradients are not as steep as they appear in part (a). (c) A three-dimensional representation of the topography plotted in parts (a) and (b).

When you study contour maps, make sure you look at the values on each of the contour lines to determine the value assigned to each contour. This will enable you to see which features are highs and lows and to assess the relative magnitude of gradients at different points on the plot accurately. Many contour plots are now produced by computers, and in some of these, contour lines are not used. Instead, the entire plot is filled with color that varies according to the value of the parameter plotted. Usually, the order of colors in the spectrum of visible light is used. Red represents the highest value, grading progressively through orange, yellow, green, and blue to violet, which represents the lowest value (Fig. 1-7). These plots are essentially contour plots that have an infinitely large number of contour lines and in which the range of values between each pair of adjacent contours is represented by a slightly different shade of color. Figure 3-3, Figure 7-11, and Figure 8-15 are additional examples of this convention. This color convention, from red to violet, is now universally accepted and makes it easy to visually identify the areas of high and low values. Consequently, with a few exceptions made for specific reasons, we have used this convention to color-code the regions between contours in all of the contour plots in this text.

Cross-sectional profiles show the distributions of properties on slices (cross sections) through, for example, the Earth or an ocean. Oceanographers commonly use cross-sectional profiles with contour plots to show the distribution of properties with depth and distance across the vertical slice. Because the oceans and the Earth’s crust are extremely thin in comparison with the widths of the oceans and continents, these profiles almost always have a large vertical exaggeration. For example, the maximum depth of the oceans is approximately 11 km, whereas their widths are several thousand kilometers. If we were to draw a vertical profile across the ocean with no vertical exaggeration on a page in this book and use an ocean depth of 11 km scaled to a height of 11 cm on the vertical axis, then the profile would have a width of 1000 cm (more than 50 page widths) for each 1000 km of ocean width plotted. Because this is obviously not possible, the scale on which distance across the ocean is plotted is reduced. This decreases the width of the plot but also introduces vertical exaggeration, which distorts the data.

Figure 1-8 shows the effects of 10 and 100 times vertical exaggerations of a topographic profile. Most profiles used in ocean sciences have exaggerations greater than 100 times. Vertically exaggerated profiles make the gradients of topographic features appear much greater than they really are. Two points are important to remember as you examine vertically exaggerated profiles in this textbook. First, the seafloor topography is much smoother, and the slopes are much shallower than depicted in the profiles. Second, ocean water masses are arranged in a series of layers that are very thin in comparison with their geographic extent, and this is not adequately conveyed by the vertically exaggerated cross-sectional profiles.

Figure 1-8. Cross-sectional vertical profiles used to depict ocean or atmospheric data are almost always vertically exaggerated. The effect of vertical exaggeration is shown in this figure. If the dark blue area below the lowest line in this graph were a plot of seafloor depth or land surface elevation, we would conclude that the topography was relatively flat. However, when vertically exaggerated 10 times (the mid blue plot area), it appears to be much more rough. When exaggerated 100 times (the light blue plot area), the topography looks like extremely rugged mountain chains with very steep slopes. Cross-sectional profiles in this book are plotted with vertical exaggerations greater than 100 times. This distortion cannot be avoided and must be considered when interpreting the data these cross sections depict.

Maps and Charts

The Earth is spherical, and the ideal way to represent its geographic features would be to depict them on the surface of a globe. Although virtual-reality computer displays make such representation possible, it is impractical for most purposes. Consequently, geographic features of the Earth’s surface are almost always represented on two-dimensional maps or charts. To represent the spherical surface of the Earth on a two-dimensional map, a projection must be used. A projection is a set of rules for drawing maps of Earth’s features on a 2-dimensional screen or a piece of paper. All projections distort geographic information, each in a different way. The projection that most people are familiar with is the Mercator projection, which was designed to be used for navigation. However, several different projections are used in this textbook, and you may see other projections elsewhere.

To draw accurate maps of the Earth, we must relate each location on the Earth’s surface to a particular location on the flat map’s surface. Therefore, we must be able to identify each point on the Earth’s surface by its own unique “address.” Latitude and longitude are used for this purpose.

In a city, the starting “address” is usually a specific point downtown, and the street numbers and house numbers on each street increase with distance from that point. On the Earth’s surface, there is no center from which to start. However, two points, the North and South Poles, are fixed (or almost so), and the equator can be easily defined as the circle around the Earth equidistant from the two poles. This is the basis for latitude. The equator is at latitude 0°, the North Pole is 90°N, and the South Pole is 90°S. Every location on the Earth other than at the poles or on the equator has a latitude between either 0° and 90°N or 0° and 90°S. Why do we use degrees (°)? Figure 1-9a shows that if we draw a circle around the Earth parallel to the equator, the angle between a line from any point on this circle to the Earth’s center (dashed line) and a line from the Earth’s center to the equator is always the same. If the circle is at the equator, this angle is 0°; if it is at the pole, the circle becomes a point, and this angle is 90°. If the circle is not at the equator or one of the poles, this angle is between 0° and 90° and is either south or north of the equator.

Figure 1-9. Latitude and longitude are measured as angles between lines drawn from the center of the Earth to the surface. (a) Latitude is measured as the angle between a line from the Earth’s center to the equator and a line from the Earth’s center to the measurement point. (b) Longitude is measured as the angle between a line from the Earth’s center to the measurement point and a line from the Earth’s center to the prime (or Greenwich) meridian, which is a line drawn from the North Pole to the South Pole passing through Greenwich, England. (c) Lines of latitude are always the same distance apart, whereas the distance between two lines of longitude varies with latitude.

Latitude can be measured without modern instruments. Polaris, the Pole Star or North Star, is located exactly over the North Pole, so at 90°N, it is directly overhead. At lower latitudes, Polaris appears lower in the sky until, at the equator, it is on the horizon (at an angle of 90° to a vertical line). In the Northern Hemisphere, we can determine latitude by measuring the angle of the Pole Star to the horizon. In the Southern Hemisphere, no star is directly overhead at the South Pole, but other nearby stars can be used and a correction made to determine latitude. Star angles can be measured accurately with very simple equipment, and the best ancient navigators were able to measure these angles with reasonable accuracy without instruments.

Latitude is a partial address of a location on the Earth. It specifies only the hemisphere, northern or southern, in which the location lies and that the location is somewhere on a circle (line of latitude) drawn around the Earth at a specific distance from the pole (equivalent to “somewhere on 32nd Street”). The other part of the address is the longitude. Figure 1-9b shows that the relative locations of two points on a line of latitude can be defined by measurement of the angle between lines drawn from the Earth’s center to each of the locations. This angle is longitude, but it has no obvious starting location. Consequently, a somewhat arbitrarily chosen starting location, the line of longitude (north-south line running between the North and South Poles) through Greenwich, England, has been agreed upon as 0° longitude and is known as the “prime meridian.”

Longitude is measured in degrees east or west of the prime meridian (Fig. 1-9b). Locations on the side of the Earth exactly opposite the prime meridian can be designated as either 180°E or 180°W. All other locations are between 0° and 180°E or between 0° and 180°W. Longitude is not as easy to measure as latitude because there is no fixed reference starting point, and no star remains overhead at any longitude as the Earth spins. The only way to measure longitude is to accurately fix the time difference between noon, when the sun is directly overhead, at the measurement location and noon at Greenwich. The Earth rotates through 360° in 24 hours, so a 1-hour time difference indicates a 15° difference in longitude. To determine longitude, the exact time (not just the time relative to the sun) must be known both at Greenwich and at the measurement location. Before radio was invented, the only way to determine the time difference was to set the time on an accurate clock at Greenwich and then carry this clock to the measurement location. Consequently, longitude could not be measured accurately until the invention of the chronometer in the 1760s.

Latitude and longitude lines provide a grid system that specifies any location on the Earth with its own address and enables us to draw maps. Before we look at these maps, notice that 1° of latitude is always the same length (distance) wherever we are on the Earth, but the distance between lines of longitude is at a maximum at the equator and decreases to zero at the poles (Fig. 1-9c).

Figure 1-10a is a familiar map of the world. This representation of the Earth’s features is a Mercator projection, which is used for most maps. In the Mercator projection, the lines of latitude and longitude are drawn as a rectangular grid. This grid distorts relative distances and areas on the Earth’s surface. The reason is that, on the Earth, the distance between two lines of longitude varies with latitude as shown in Figure 1-10c, but the Mercator projection shows this distance as the same at all latitudes. Furthermore, the Mercator projection shows the distance between lines of latitude to be greater at high latitudes than near the equator, even though on the Earth’s surface, they are the same.

Figure 1-10. Typical map projections. (a) Mercator projection. Higher latitudes near 90°N and 90°S are not shown because the shape and area distortions introduced by this projection increase rapidly with latitude near the poles. (b) Goode’s interrupted projection preserves relative areas and shows each of the oceans without interruption. However, it distorts the shapes of the continents. (c) Robinson projection. This projection preserves none of the four desirable characteristics perfectly, but it is a good approximation for many purposes.

Why, then, has the Mercator projection been used for so long? The answer is that it preserves one characteristic that is important to travelers: on this projection, the angle between any two points and a north-south line can be used as a constant compass heading to travel between the points. However, the constant-compass-heading path is not the shortest distance between the two points. The shortest distance is a great-circle route. A great circle is any circle around the full circumference of the Earth. For navigation, this great circle passes through both the starting and end point of the journey. The Mercator projection suggests that the “direct” route between San Francisco and Tokyo is almost directly east to west. However, the normal flight path for this route is almost a great-circle route that passes very close to Alaska and the Aleutian Islands. You can see the great-circle route and why it is the shortest distance by stretching a piece of string between these two cities on a globe. Over short distances, the compass-direction route and the great-circle route are not substantially different in terms of distance, and the simplicity of using a single, unchanging compass heading makes navigation easy. Ships and planes now use computers to navigate over great-circle routes that require them to fly or sail on a continuously changing compass heading.

Although the Mercator projection is very widely used, other projections preserve different characteristics of the real spherical world. The following four characteristics are desirable to preserve in a map projection:

• Relative distances. Measured distance between any two points on the map can be calculated by multiplying by a single scale factor. Most projections do not preserve this characteristic.
• Direction. Compass directions derived from the straight lines between points on the map could be used for navigation. The Mercator projection preserves this characteristic.
• Area. Two areas of the same size on the Earth would be equal in area on the map. The Mercator projection is one of many projections that do not preserve this characteristic.
• Shape. The general shape of the oceans and land masses on a map would be similar to the shapes of these features on the globe. Most projections do not preserve this characteristic.

Because no projection (only a globe) preserves all four of these characteristics, different projections are used for different purposes. In this textbook, for example, Goode’s interrupted projection (Fig. 1-10b) is used often because it preserves relative areas correctly and shows each of the three major oceans uninterrupted by the edge of the map. Other projections, such as the Robinson projection (Fig. 1-10c), are also used in this textbook. The projection used for each map is identified in each figure. Table 1-1 lists the relative ability of each of these projections to satisfy the four desirable map characteristics described here.

 

Table 1-1. Characteristics of Selected Map Projections

Projection	Preserves Relative Distances	Preserves Directions	Preserves Relative Areas	Preserves Shape	Areas Most Distorted	Common Uses
Mercator	Poor	Excellent	Poor	Fair	Mid to high latitudes	Navigation charts, world maps, maps of limited areas
Miller’s cylindrical	Good	Good	Excellent	Poor	High latitudes	World maps
Robinson	Good	Fair	Good	Fair	High latitudes, 4 “corners”	World maps
Mollweide	Good	Fair	Good	Poor	High latitudes, 4 “corners”	World maps
Goode’s interrupted	Good	Poor	Very good	Poor in most areas	Relative positions of continents	World maps, global oceans
Conic	Good	Excellent	Very good	Excellent	Distortion equally distributed	Maps of the U.S., individual continents
Polar azimuthal	Fair	Excellent	Good/poor	Good	Outer edges	Maps of polar regions

 

 

 

The Size and Shape of Greenland

How big is Greenland compared to the United States? If you said that it was similar in size, you are among the majority. Due to the extensive use of the Mercator projection, many people today mistakenly believe that Greenland is larger than it actually is. What is a projection, you ask? Well, the Earth is round, and a map is flat, so changes in shape, area, or direction are necessary to see the whole Earth at once on a map. The Mercator projection makes all of the vertical lines of longitude parallel to each other, which is not accurate, especially near the poles. The Mercator projection transforms the Earth’s surface into a rectangle, which is convenient for printing, computer monitors, and using a compass on an ocean voyage, but it significantly distorts the area near the poles.

Take a look at the maps in Figure 1-11 with the U.S. overlaid by Greenland. What do you notice about the longitude lines? Which map has curved lines, which are closer to the reality of a globe?

Figure 1-1B1. Map projections distort the surface of the Earth differently to show it on a flat map. The (a) Mercator projection shows the longitude lines as straight, vertical lines, while the (b) Orographic projection shows the lines of longitude as curves that meet at the north pole. Greenland, as viewed in each projection, is overlaid in red over the U.S. to illustrate the difference in scale between the two projections.

We use Greenland as an example because it is close to the North Pole and is therefore stretched significantly, both vertically and horizontally, in the Mercator projection. In Figure 1-11a, Greenland looks nearly as large as North America. In contrast, Greenland is not significantly stretched in the orographic projection and appears much closer to its actual size and shape in Figure 1-11b. The distortion in these features near the poles prompts us to view them differently, so several developing nations, especially those near the equator, have suggested that world maps should not use the Mercator projection. Why do you think that is?

 

Scientific Notation and Units

Some of the numbers mentioned in this chapter are extremely large. For example, the history of the Earth presented in Figure 1-4 spans nearly 5 billion (5,000,000,000) years. On that figure, the abbreviation MYA was used to represent millions of years ago. In ocean sciences, such large numbers are common, as are very small numbers. For example, the concentration of lead in seawater is about 0.000,000,000,5 gram per kilogram of water. In order to avoid using long strings of zeros, scientists use a type of shorthand for numbers like these. For example, the age of the universe is 1.4•10¹⁰ years, and the concentration of lead in seawater is 5•10^–10 grams per kilogram.

These numbers might look odd, but they are really quite simple. The numbers are written using powers of 10. The • symbol can be stated as “times” or “mutiplied by” and is always followed by 10, so together they make “times ten” or “multiplied by ten”. The superscript number that always follows the 10, represents the number of orders of magnitude (factors of 10) by which the digit before the •10 must be multiplied. Thus, 5•10⁹ is 5 multiplied by ten, nine times (5×10×10×10×10×10×10×10×10×10) which is usually shortened to 5 times ten to the 9th. A quicker way to use this notation is to take the number before the •10 and add nine zeros. The number is said to be raised by 9 orders of magnitude (powers of 10). Similarly, 5•10^–10 is 5 times ten to the power of negative 10 (the number is multiplied by 0.000,000,000,1, which gives 0.000,000,000,5. Notice that the negative sign in the superscript part of the scientific notation denotes the number of powers of 10 by which the number is reduced. When a number has more than one nonzero digit, such as 5,230,000,000, the scientific notation becomes 5.23•10⁹. The scientific notation places one nonzero digit to the left of the decimal so, in this example (5.23) the simple way to use the notation is to move the decimal point 9 times, adding zeros only after the decimal point has passed the numbers to the right of the decimal point in the scientific notation (23 in our example). Notice that this shorthand system makes it easy to compare two very large or two very small numbers. In our example, it is easy to see that 5•109 and 5.23•10⁹ are not very different without having to count all the zeros. Similarly, 5•10⁹ is clearly much larger than 5.23•10⁷. This text makes extensive use of scientific notation. Appendix 1 provides a simple conversion table if you need it.

Like other scientists, oceanographers use a variety of scientific units to identify such parameters as length, speed, and time. To avoid problems with unit conversions, such as miles to kilometers, and to make the comparison of data easier, scientists have developed an International System of Units (SI) that is steadily progressing toward being used universally, although some other units are still widely used. The seven SI base units are shown in Table 1-2.

 

Table 1-2. Base SI units

Parameter	Unit	Symbol
Length	meter	m
Mass	kilogram	kg
Electric current	ampere	A
Thermodynamic temperature	kelvin	K
Amount of a substance	mole	mol
Luminuos intensity	candela	cd

All other units are “derived” units. For example, volume is measured in cubic meters (m³), and speed is measured in meters per second (m/s or m•s^–1). SI units are used in much of this text. However, as is still common in science, they are not used exclusively because some of them remain unfamiliar even to many members of the scientific community. Appendix 1 includes more information about SI units and a table of all scientific unit abbreviations used in this text.

In this text, we use simple SI units to express concentrations of chemicals dissolved in water, for example, grams per kilogram (g•kg^–1) or milligrams per kilogram (mg•kg^–1). However, you may see on the web or in other publications concentrations expressed in molality or molarity. Molality is simply the concentration of the dissolved substance in grams of dissolved substance per kilogram (g•kg^–1) divided by the molecular weight of the dissolved substance. Molarity is calculated in the same way but uses the concentration of dissolved substance per liter and is expressed in grams of dissolved substances per liter (g•l^–1). Dividing the mass of a substance by its molecular weight gives you the amount of substance in “moles,” a unit that is related to the number of molecules of the substance present – so 1 mole of a substance has exactly the same number of molecules as 1 mole of any other substance. Chemists use molality or molarity because it can simplify some calculations.

For example, seawater contains about 19.8 g•kg^–1 of chlorine, present as the chloride ion (Cl^–)ion, and about 10.78g•kg^–1 of sodium as the sodium ion (Na+). This looks like it is a lot more chloride ion than sodium ion but, if we convert these to molality (by dividing each number by the molecular weight of the ion - about 35 for the chloride ion and 23 for the sodium ion, we find that chloride concentration in seawater is 0.55 molal and sodium is 0.47 molal - much closer. In fact, if seawater contained only dissolved sodium chloride, these molarity numbers would be the same, so we know that 0.08 moles (0.55 molal minus 0.47 molal) of other positive ions, such as potassium (K⁺) and calcium (Ca²⁺), must be present in seawater. In this example, molality (or molarity) is an expression of the number of atoms of sodium or chlorine. If we wanted to make sodium chloride from chlorine and sodium, we would need to add 1 mole of each to get 1 mole of sodium chloride, which is simpler to calculate than adding 35.5 g of chlorine and 22.99 g of sodium as we would have to do otherwise. With more complex molecules than sodium chloride, this simplification becomes even more valuable.