Initial Publication Date: August 11, 2023 | Revision: August 7, 2024 (see revision history: 2 events)

Ternary Diagrams: Practice Problems
Solving Earth Science Problems with Ternary Diagrams

Plotting Data on Ternary Diagrams

Sedimentology: Sediment classification

Sedimentologists have their own classification scheme for sediments that is based on grain size, called the Shepherd Classification (shown at right). The Shepherd Classification is most often applied to sediments with minimal organic components or those found in an offshore environment.

Problem 1: You have taken a core sample of sediment from the Gulf of Mexico and are interested in classifying the sample based on the Shepherd Classification (see ternary at right). You run your sample through a set of sieves to separate them by grain size. After sieving, you weigh the sediments and create a table (shown to the left of the Shepherd Classification diagram). Using that data, how would you classify your sample (what name would you give the sediments) using the Shepherd Classification?

Show me how to classify my sample

Step 0: Overlay (or construct) the grid showing equal fractions of each component.

Show me how for the Shepherd Classification diagram'

Step 1: Determine the components shown on the diagram (there will be three), which apex reflects 100% of each component (and which sides of the diagram show the proportions of each component). If the sides of the diagram are not labeled, you will need to decide which side of the triangle will show percentages for each component.

Show me how for the Shepherd Classification diagram

For the Shepherd Classification, the three components of interest are clay, silt, and sand.

100% clay is at the top apex (and proportions are labeled on the right side of the triangle).
100% silt is at the right apex of the triangle (and percentages are labeled on the bottom side of the triangle).
100% sand is at the left apex of the triangle (and percentages are labeled on the left side of the triangle).
Numbers increase in a counterclockwise direction and components are labeled on each side.

Step 2. If the problem gives you more than three components, determine which components in the problem are relevant to the ternary diagram of interest. If the problem only lists the three components shown on the diagram, you can skip to step 3.

Show me how for the Shepherd Classification diagram

The sediment analysis includes four components: gravel, sand, silt, and clay. Soil textures are classified by the grain sizes of the mineral components of the sample, which only include sand, silt, and clay (circled on the diagram). For the rest of this problem, you can ignore gravel (crossed off in the table). For steps 3–6, you will need to know that your sample contains 35 g sand, 63 g silt, and 36 g clay.

Step 3. Normalize the data into percentages of each component. To normalize, divide the amount (weight, fraction, value, etc.) of each component by the total amount (weight, fraction, value, etc.) of all three components. Equations to normalize components:

Show me how for the Shepherd Classification diagram

To find the percentage of sand, divide the weight of sand by the total weight of the sample:

`% "sand" = (35 g)/((35 g + 63 g + 36 g)) " * " 100 = (35 g)/(134 g) " * " 100 = 26%`

To find the percentage of silt, divide the weight of silt by the total weight of the sample:

`% "silt" = (63 g)/((35 g + 63 g + 36 g)) " * " 100 = (63 g)/(134 g) " * " 100 = 47%`

To find the percentage of clay, divide the weight of clay by the total weight of the sample:

`% "clay" = (36 g)/((35 g + 63 g + 36 g)) " * " 100 = (36 g)/(50g) " * " 100 = 27%`

Notice that `% "sand" + % "silt" + % "clay" = 26% + 47% + 27% = 100%`

Step 4: Draw a line that represents the proportion of one end-member component at the appropriate percentage and so that it is parallel to the side opposite the apex, representing 100% of that end-member. In some cases, you may have to approximate (interpolate) the location of the line for percentages between those that are labeled.

Show me how for the Shepherd Classification diagram

Let's start with sand (see step 4a for other components). Note that lines parallel to the right side of the triangle and numbers along the left side of the diagram represent the proportion of sand. Above, you calculated that there was 26% sand in your sediment sample, so you will need to draw a line that intersects the left side of the triangle at 26% sand and is parallel to the right side (purple dashed line).

Step 4a: Repeat the above process for the other two components. Your lines should intersect at a single point representing the sample composition.

Show me how for the Shepherd Classification diagram

For this diagram, lines parallel to the left side of the triangle (and numbers along the bottom side) represent proportions of silt. You calculated that 47% of your sample was made up of silt, so find the point on the bottom side of the diagram that represents 47% silt. Then draw (or sketch in) a line parallel to the left side of the triangle (red dotted line).

Finally, to plot clay, note that lines parallel to the bottom side of the triangle (and numbers along the right side) correspond to proportions of clay. In step 3 you calculated that 27% of your sample was clay, so, you find the point on the right side of the diagram that represents 27% silt and draw a line that intersects the left side of the triangle at 27% silt and parallel to the bottom side of the diagram (yellow dashed and dotted line)

Step 5: Plot the normalized data as a single point.

Show me how for the Shepherd Classification diagram

The sample composition is represented where the lines cross. When the lines in the images above have been removed, the green star is plotted as the composition of the sediment described above.

Step 6: Interpret the data plotted on the diagram.

Show me how for the Shepherd Classification diagram

Mineralogy: Plotting pyroxene compositions

Many mineral groups that exhibit solid solution (e.g., feldspar, pyroxene, amphibole, etc.) can be plotted on a ternary diagram with respect to three main components to differentiate between different mineral species.

Problem 2: You have analyzed pyroxene in an igneous rock sample that you collected for your senior thesis. You are interested to know what type of pyroxene is present in your sample, which can give you information about the tectonic setting, pressure, and temperatures at which the igneous rock crystallized. Your chemical data (collected on the electron microprobed) is shown (as weight percent of oxides found in pyroxene) in the table with the figure at right. The diagram in the figure (right) is a ternary diagram that can be used to plot pyroxene compositions.

Note: The white spaces on this diagram do not have any fields labeled. That is because any data that does not plot in the gray areas on this ternary diagram is not a pyroxene.

Show me information about pyroxene compositions

Pyroxene compositions are dependent on the crystalline structure of pyroxene molecules. There are two sites within the structure of pyroxene that can accommodate ions with a 2+ charge (Ca, Mg, and Fe all have 2+ charges and bond with one oxygen). Only one of those sites can accommodate CaO (or FeO or MgO), so if CaO is present, it occupies most of those sites (if not, those sites are filled with varying amounts of FeO and MgO). Other sites can only accommodate FeO and MgO. Pyroxenes that contain CaO are called clinopyroxenes; those that only contain Feo and MgO are called orthopyroxenes.

Determine the type of pyroxene (name) in your igneous rock using the pyroxene diagram and table of oxide compositions shown in the figure above.

Show me the steps for plotting pyroxene compositions

Step 0: Overlay (or construct) the grid showing equal fractions of each component.

Show me how for the pyroxene diagram

This diagram has "tick marks" showing 10% increments along each side, but the numbers and grid are missing. You will need to construct a grid by connecting the tick marks on either side of the diagram to make a grid so you can plot your compositions.

Show me how for the pyroxene diagram

For pyroxene, the three components of interest are CaO, MgO, and FeO. On this diagram, the apices are labeled, but the sides of the triangle are not, so you will need to decide how to label the grid you constructed in Step 0. The figure below shows them labeled, increasing in a clockwise direction, but you could just as easily label them in a counterclockwise direction.

100% CaO is at the top apex (and the figure here shows percentages labeled in purple on the left side of the triangle).
100% FeO is at the right apex of the triangle (and the figure here shows percentages labeled in red on the right side of the triangle).
100% MgO is at the left apex of the triangle (and the figure here shows percentages labeled in blue on the bottom side of the triangle).
Numbers increase in a clockwise direction and components are labeled on each side.

Show me how for the pyroxene diagram

The table of weight percent (wt%) has data that you do not need (SiO₂, Al₂O₃, and MnO), so you can ignore those components of pyroxene for this problem (they are crossed off in the figure to the right). You will only be dealing with the components on this diagram: CaO, MgO and FeO. For steps 3–6, you will need to know that your pyroxene contains 18.31 wt% CaO, 14.31 wt% MgO, and 12.06 wt% FeO.

Show me how for the pyroxene diagram

Step 4: Draw a line that represents the proportion of one end-member component at the appropriate percentage and so that it is parallel to the side opposite the apex representing 100% of that end-member. In some cases, you may have to approximate (interpolate) the location of the line for percentages between those that are labeled.

Show me how for the pyroxene diagram

Let's start with CaO (see Step 3 for other components). Note that horizontal lines (those parallel to the bottom side of the triangle) and numbers along the left side of the diagram represent the proportion of CaO. Above, you calculated that there was 41% CaO in your soil sample, so you will need to draw a line that intersects the left side of the triangle at 41% CaO and that is parallel to the bottom side (dashed line labeled CaO = 41%).

Step 4a: Repeat the above process for the other two components. Your lines should intersect at a single point, representing the sample composition.

Show me how for the pyroxene diagram

For this diagram, lines parallel to the right side of the triangle (and numbers along the bottom) represent proportions of MgO. You calculated that 32% of your sample was made up of MgO, so approximate the point between 30 and 40 on the bottom of the diagram that represents 32% MgO. Then draw (or sketch in) a line parallel to the right side of the triangle (see dashed line labeled MgO=32%).

Finally, to plot FeO, note that lines parallel to the left side of the triangle (and numbers along the right side) correspond to proportions of FeO. In Step 3 you calculated that 27% of your sample was made up of FeO, so you will need to approximate the point between 20 and 30 that represents 27% FeO and draw a line that intersects the right side of the triangle at 27% FeO and that is parallel to the left side of the diagram (see dashed line labeled FeO = 27%). A red star has been placed where all three lines cross

Step 5. Plot the normalized data as a single point. Determine where your lines cross and place the point there.

Show me how for the pyroxene diagram

When all three lines are placed on the plot, they cross at a single point, shown as a red star below.

Step 6: Interpret the data plotted on the diagram.

Show me how for the pyroxene diagram

Interpreting Points Plotted on Ternary Diagrams

Petrology: Extracting and interpreting plotted rock compositions

Problem 3. A colleague collected some igneous plutonic (coarse-grained/intrusive) rocks (with no feldspathoid) in a field area for a project you are working on. This colleague has plotted the rocks on the ternary diagram below (also known as the IUGS [International Union of Geological Sciences] or Streckheisen diagram) so that you can classify the rocks. The colleague has also color coded the rocks by age: red circle = oldest; yellow square = middle; and blue triangle = youngest. Based on your colleague's analysis, the rocks collected are classified as quartz monzonite (red, oldest), granodiorite (yellow), and granite (blue, youngest).

You are interested in better characterizing the mineral composition of these rocks, so you can say something about how the mineralogy evolved during crystallization. As a result, you want to know how much of each mineral on this diagram is present in the collected rocks. Use the information below to determine the relative percentages of minerals.

Show me how to determine the composition of each of the rocks

Step 0: Overlay (or construct) the grid showing equal fractions of each component.

Show me how for the IUGS diagram

This diagram has no markings to tell you where to put the grid lines.

Begin by marking 10 equal increments on each side (you can label them with percentages as in the image to the left).

Connect lines parallel to each side and connecting marks you made to create a grid.

Step 1: Determine the components shown on the diagram (there will be three) and which apex reflects 100% of each component.

Show me how for the IUGS diagram

For plutonic rocks (with quartz), the three components of interest are quartz (Q), alkali feldspar (A), and plagioclase (P). On this diagram, the apices were labeled, but the sides of the triangle were not. In the image below, the sides are labeled increasing in a clockwise direction, so we will use that convention in the rest of the problem.

100% quartz (Q) is at the top apex (and the figure here shows percentages labeled in purple on the left side of the triangle).
100% plagioclase (P) is at the right apex of the triangle (and the figure here shows percentages labeled in red on the right side of the triangle).
100% alkali feldspar is at the left apex of the triangle (and the figure here shows percentages labeled in blue on the bottom side of the triangle).

Step 2: Draw three lines through each point and parallel to grid lines to determine the relative abundances of each end member.

Show me how for the IUGS diagram

Let's begin with the proportion of quartz in each of the rocks plotted here. Quartz percentages are represented by the horizontal lines on the grid. Draw a line through each point of interest and parallel to the bottom side of the triangle. Read the percentages of each rock from the left side of the diagram :

for the red circle (quartz monzonite): 10% quartz.
for the yellow square (granodiorite): 25% quartz.
for the blue triangle (granite): 40% quartz.

Next let's determine the proportion of plagioclase in the rocks plotted on the diagram. Plagioclase percentages are represented by the lines parallel to the left side of the triangle. Draw a line through each point of interest and parallel to the left side of the triangle. Read the percentages of plagioclase in each rock from the right side of the diagram:

for the red circle (quartz monzonite): 65% plagioclase.
for the yellow square (granodiorite): 50% plagioclase.
for the blue triangle (granite): 35% plagioclase.

Finally, let's determine the proportion of alkali feldspar in these rocks. Alkali feldspar percentages are represented by the lines parallel to the right side of the triangle. Draw a line through each point of interest and parallel to the right side of the triangle. Read the percentages for alkali feldspar in each of the rocks from the bottom of the diagram: for all compositions: 25% alkali feldspar.

Step 3: Record the percentages of each end member component, confirming that they sum to 100%.

Show me how for the IUGS diagram

Step 4: Interpret your findings. Use what you have learned to answer the question posed.

Show me how for the IUGS diagram

You are interested in the changes in mineralogy through time. You can observe that the amount of alkali feldspar stays the same through time. However, the amount of quartz increases and the amount of plagioclase decreases through time (from red through yellow to blue).

Your samples are becoming more quartz-rich and depleted in plagioclase. This change through time—enrichment in quartz and depletion in plagioclase—is seen in many igneous intrusions, including the igneous intrusions that make up Yosemite National Park (pictured to the right). As fractional crystallization progresses, Ca-rich plagioclase (and other "mafic components") crystallizes early, enriching the magma in other elements (like the alkalies and SiO₂). The magma becomes more quartz (SiO₂) rich through time.

Environmental geochemistry: Water quality

Geochemists often look at ions (or ionic groups) dissolved in freshwater to determine whether the water is safe, the source of the water, or how water chemistry changes spatially and through time. Freshwater commonly contains the dissolved cationsCations are ions, or charged particles with a positive charge. Ca⁺², Mg⁺², Na⁺, and K⁺ and the anions Anions are ions, or charged particles with a negative charge. or anionic groupsAnionic groups are a group of atoms with a negative charge. Cl^-, HCO₃^-, SO₄^-2. Major ion composition (cations and anions/anionic groups) can be plotted on ternary diagrams to characterize differences in chemistry, safety of the water, and sometimes the source of the water.

Problem 4: Watersheds in ice-free areas of western Greenland get their freshwater from either ice melt (proglacial) or precipitation (nonglacial). Proglacial and nonglacial watersheds have distinct chemical compositions; that is, the anionic compositions are different for each type of water produced. The ternary diagram for differentiating proglacial and nonglacial watersheds is shown in the ternary to the right with samples from proglacial (blue triangles) and nonglacial (red circles) watersheds plotted.

Use these data to answer the following questions:

a) Which anion (Cl^-, SO₄^-2, or HCO₃^-) is most abundant in proglacial watersheds?

b) Which anion (Cl^-, SO₄^-2, or HCO₃^-) is most abundant in nonglacial watersheds?

c) How could you use the information above to determine whether water in another watershed is proglacial or nonglacial?

Show me how to determine the compositions of Greenland's watersheds

Step 0: Overlay (or construct) the grid showing equal fractions of each component.

Show me how for the water chemistry diagram

Step 1: Determine the components shown on the diagram (there will be three) and which apex reflects 100% of each component.

Show me how for the water chemistry diagram

For water chemistry, the three components of interest are SO₄^-2 (sulfate), Cl^- (chloride), and HCO₃^- (bicarbonate). On this diagram, the apices are labeled. In the image below, the sides are labeled increasing in a counterclockwise direction, so we will use that convention in the rest of the problem.

100% SO₄^-2 is at the top apex (and the figure here shows percentages labeled on the right side of the triangle).
100% Cl^- is at the right apex of the triangle (and the figure here shows percentages labeled on the bottom side of the triangle).
100% HCO₃^- is at the left apex of the triangle (and the figure here shows percentages labeled on the left side of the triangle).

Step 2: Draw three lines through each point and parallel to grid lines to determine the relative abundances of each end member.

Show me how for the water chemistry diagram

Because we are interested in the ranges of compositions for each type of watershed, we will determine the range of compositions for proglacial (blue triangles) and nonglacial (red circles) watersheds. Let's begin with the proportion of SO₄^-2 for the parabolic dunes plotted here. Sulfate percentages are represented by the horizontal lines on the grid. For each group of samples, draw a line through the point with the lowest SO₄^-2 and through the point with the highest SO₄^-2, showing the range of compositions for that group of samples.

For nonglacial watersheds, the SO₄^-2 composition ranges from 48% to 74%.
For proglacial watersheds, the SO₄^-2 composition ranges from 9% to 17%.

Next let's determine the proportion of Cl^- in the rocks plotted on the diagram. Chloride percentages are represented by the lines parallel to the left side of the triangle. For each group of samples, draw a line through the point with the lowest Cl^- and through the point with the highest Cl^-, showing the range of compositions for that group of samples:

For nonglacial watersheds, the Cl^-composition ranges from 9% to 15%.
For proglacial watersheds, the Cl^- composition ranges from 1% to 3%.

Finally, let's determine the proportion of HCO₃^- in the rocks plotted on the diagram. Bicarbonate percentages are represented by the lines parallel to the right side of the triangle. For each group of samples, draw a line through the point with the lowest HCO₃^- and through the point with the highest HCO₃^-, showing the range of compositions for that group of samples:

For nonglacial watersheds, the HCO₃^-composition ranges from 11% to 43%.
For proglacial watersheds, the HCO₃^- composition ranges from about 80% to 90%.

Step 3: Record the percentages of each end member component, confirming that they sum to 100%.

Show me how for the water chemistry diagram

This interpretation is a bit more complicated since we determined the range for each group of samples. We can still make sure that values for each end of the range sum to 100%.

For nonglacial watersheds:
- on one end: 74% SO₄^-2 + 15% Cl^- + 11% HCO₃^-=100%
- on the other end: 48% SO₄^-2 + 9% Cl^- + 43% HCO₃^- =100%
For proglacial watersheds
- on one end: 9% SO₄^-2 + 1% Cl^- + 90% HCO₃^- =100%
- on the other end: 17% SO₄^-2 + 3% Cl^- + 80% HCO₃^- =100%

Step 4: Interpret your findings. Use what you have learned to answer the questions posed.

Show me how for the water chemistry diagram

a) Which anion (Cl^-, SO₄^-2, or HCO₃^-) is most abundant in proglacial watersheds?

Based on the information above, proglacial watersheds have the highest percentages of HCO₃^-, with somewhere in the range of 80–90%.

b) Which anion (Cl^-, SO₄^-2, or HCO₃^-) is most abundant in nonglacial watersheds?

Based on the information above, nonglacial watersheds have the highest percentages of SO₄^-2, with somewhere in the range of 48–74%.

c) How could you use the information above to determine whether water in another watershed is proglacial or nonglacial?

Based on the percentages, watersheds with proglacial water have high amounts of bicarbonate, whereas the water in nonglacial watersheds is rich in sulfate. So, determining the amounts of these anionic groups in freshwater systems near glaciers could help to determine the source of the water.

A More Complex Example: Reading and Plotting

Geomorphology: Dune types

There are many variables that can influence the formation of sand dunes, including topography, climate, humidity, vegetation, availability of sand, and wind strength and direction. The interplay of many of these variables produces different shapes and forms of sand dunes. Geomorphologists use the ternary diagram below to characterize the relationship of dune forms (morphology), vegetative cover, supply of sand, and the strength of the wind.

Problem 5: The photo of the dunes shown in the left portion of the figure below was taken in Oregon Dunes National Recreation Area. In the area near the coastal forest, the interplay of variables that control dune shape is reflected by the location of the blue dot on the dune morphology diagram on the right side of the diagram below. Given the placement of the blue dot, most of the dunes near the coastal forest in Oregon Dunes are classified as parabolic dunes. Your first job is to determine the conditions that produce the parabolic dunes shown in the photo by determining the proportions of the end-members.

Additionally, geomorphologists might want to know how changing one variable might alter the types of dunes that would be present, and so might consider questions like: what would happen if we logged the coastal forest (and reduced vegetation)? So your second job is to plot a new point that reflects reduced vegetation (more information in the question below). Let's use the dune morphology diagram to think about both the conditions that are currently present (the blue dot) and what might happen if we changed the amount of vegetation.

This question involves interpreting the plotted blue point, and plotting a new point that reflects less vegetation. So, the steps outlined below are not exactly what we've been using above. The steps are notated with "interpreting" and "plotting" so that you know where those steps come from.

Show me how to interpret the dune morphology diagram

Let's start by figuring out: What conditions are currently present to produce parabolic dunes (blue dot) near the coastal forest in Oregon Dunes National Recreation Area? (interpreting the plotted point)

Step 0 (interpreting/plotting): Overlay (or construct) the grid showing equal fractions of each component.

Show me how for the dune morphology diagram

Step 1 (interpreting/plotting): Determine the components shown on the diagram (there will be three) and which apex reflects 100% of each component.

Show me how for the dune morphology diagram

For dune morphology, the three components of interest are strength of the wind (Wind), aggressiveness of vegetation (Vegetation), and supply of sand available (Supply of Sand). On this diagram, the apices were labeled. In the image below, the sides are labeled, increasing in a counterclockwise direction, so we will use that convention in the rest of the problem.

100% Wind is at the top apex (and the figure here shows percentages labeled in purple on the right side of the triangle).
100% Vegetation is at the right apex of the triangle (and the figure here shows percentages labeled in blue on the bottom side of the triangle).
100% Supply of Sand is at the left apex of the triangle (and the figure here shows percentages labeled in red on the left side of the triangle).

Step 2 (interpreting): Draw three lines through each point and parallel to grid lines to determine the relative abundances of each end-member.

Show me how for the dune morphology diagram

Let's begin with the proportion of Wind for the parabolic dunes plotted here. Wind strength percentages are represented by the horizontal lines on the grid. Draw a line through the point of interest and parallel to the bottom side of the triangle. Read the percentages from the right side of the diagram: 20% wind.

Next let's determine the proportion of Vegetation in the rocks plotted on the diagram. Vegetation percentages are represented by the lines parallel to the left side of the triangle. Draw a line through each point of interest and parallel to the left side of the triangle. Read the percentages from the bottom of the diagram: 34% vegetation

Finally, let's determine the proportion of Supply of Sand in these rocks. Supply of Sand percentages are represented by the lines parallel to the right side of the triangle. Draw a line through each point of interest and parallel to the right side of the triangle. Read the percentages from the left side of the diagram: 46% Supply of Sand.

Step 3 (interpreting): Record the percentages of each end member component, confirming that they sum to 100%.

Show me how for the dune morphology diagram

Next, let's think about: what would happen if we logged the coastal forest and reduced the vegetation present in this area? (plotting a new point) For the purposes of this question we know that the vegetation is reduced (let's say vegetation was reduced to 30% of its original value, and it now plots at 10% on this diagram). The wind conditions are probably not going to change significantly, so let's say that number doesn't change. With that information, plot a new point that represents conditions and determine the type of dune that would be present after logging.

Note: We have already done steps 0 and 1 for plotting above.

Step 4 (plotting step 3). Normalize the data into percentages of each component so they sum to 100%.

Show me how for the dune ternary

The question above actually only gives us information about the vegetation and the wind:

Vegetation for this new plot = 10% vegetation (see question above)
Wind for this new point = 20% wind (see Step 2 above)

We know that the totals must normalize to 100%, so we can figure out the value for "sand supply" by subtracting what we have from 100%:

100% total - 10% wind - 20% wind = 70% sand supply.

Step 5 (plotting step 4): Draw a line that represents the proportion of one end-member component at the appropriate percentage and so that it is parallel to the side opposite the apex representing 100% of that end-member. In some cases, you may have to approximate (interpolate) the location of the line for percentages between those that are labeled.

Show me how for the dune morphology diagram

Let's start with wind (see Step 4 for other components). Note that lines parallel to the bottom side of the triangle and numbers along the right side of the triangle represent the proportion of wind. Above, you calculated that there was 20% wind for this area, so you will need to draw a line that intersects the right side of the triangle at 20% wind and is parallel to the bottom side (see bold purple line).

Step 5a (plotting Step 4): Repeat the above process for the other two components. Your lines should intersect at a single point representing the sample composition.

Show me how for the dune morphology diagram

For this diagram, lines parallel to the left side of the triangle (and numbers along the bottom side) represent proportions of vegetation. The information above indicates that vegetation makes up 10% of the newly logged ecosystem, so find the point on the bottom side of the diagram that represents 10% vegetation. Then draw (or sketch in) a line parallel to the left side of the triangle (bold blue line).

Finally, to plot sand supply, note that lines parallel to the right side of the triangle (and numbers along the left side) correspond to sand supply proportions in this system. In step 4 above, you calculated that sand supply constituted 70% of the system, so, find the point on the left side of the diagram that represents 70% sand supply and draw a line parallel to the right side of the triangle (bold red line)

Step 6: Plot the normalized data as a single point.

Show me how for the dune morphology diagram

The new conditions described above can be plotted where all three lines cross in the example above. When the lines in the images above have been removed, the orange star represents the conditions present when vegetation has been reduced significantly.

Step 7 (interpreting/plotting Step 6): Interpret the data plotted on the diagram. Use what you have learned to answer the questions posed.

Show me how for the dune morphology diagram

Part 1 (reading the point): Based on your interpretation, the conditions that produce the parabolic dunes in Oregon Dunes National Recreational area are 20% wind + 34% vegetation + 46% sand supply.

Part 2 (plotting a new point with less vegetation): Based on the newly plotted data with about 30% of the original vegetation, your new conditions (orange star) plot in the field for transverse dunes. Therefore, you can conclude that logging this area would likely change the dune morphology from parabolic to transverse dunes.