Homework Problem # 1 - 50 points
Due February 19, Friday in class

Part I: ESSAY (25 points)
The "four classic eruptions" in Chapter 4 of your text are the focus of this part of your homework: the 79 AD eruption of Vesuvius in Italy, the 1883 eruption of Krakatau in Indonesia, the 1902 eruption of Mt. Pele'e in the West Indies, and the 1980 eruption of Mt. St Helens in Washington state.
Read this chapter and supply the following information for each of these four volcanoes. Additional information may also be found in Chapter 17 of your text. You may need to look up other information in books on volcanoes at the Henderson Library. I will put "Volcanoes of the world" by Simkin and Siebert in my mailbox in the Geology and Geography Office. You may use this as an additional resource, if needed. As a courtesy to me and your peers, please do not take this book away from the office.

a) volume of lava erupted
b) volume of tephra erupted
c) towns and sub regions affected by the eruption as described in your text
d) climactic effect of the eruption (during the following year(s))
e) type of eruption (Hawaiian, Strombolian, Plinian, Vulcanian, etc.)
f) volcanic explosivity index (VEI)
g) number of fatalities

Please report your findings in complete sentences, paragraph form (one paragraph for each volcano). Emphasis will be placed on clarity and quality of your essay. Please be sure to spell check your essay. No hand written essay will be accepted.

Part II: Forecasting the next Mauna Loa eruption (25 points)
Data and the text for this exercise is borrowed from Dr. Steve Mattox (Grand Valley State University, MI) from a paper submitted to Journal of Geological Education in 1998.

PURPOSE

Mauna Loa, on the island of Hawaii, is one of the most studied volcanoes on Earth. Based on Mauna Loa's long historic record and detailed geologic mapping, volcanologists have published forecasts for future activity at the volcano. This inquiry-based exercise requires students to think like scientists while interpreting data about Mauna Loa's past activity.

INTRODUCTION

Mauna Loa, the largest shield volcano on Earth, has been the focus of long and detailed study (Rhodes and Lockwood, 1995). A wealth of information is available on the volcano's 39 historic eruptions including location of vents, duration of eruptions, and the volume of lava erupted. Volcanologists use past eruption patterns to forecast future activity at active volcanoes (Decker, 1986). Decker and others (1995) applied this method to Mauna Loa to forecast the probability of future eruptions. Lockwood (1990) used vent migration patterns to suggest a location for the next vent that forms on the northeast rift zone. King (1989) constructed a model to predict the volume of Mauna Loa eruptions.

WHEN WILL MAUNA LOA ERUPT AGAIN?

Understanding the concept of recurrence time is critical to providing forecasts of future activity at the volcano. Recurrence time is the time interval from the onset of one eruption to the onset of the next eruption. Mean recurrence time is the average of all known recurrence times for a volcano. Volcanologist Robert Decker draws an analogy between eruptions and cutting cards: the next eruption should not occur every mean recurrence time any more than cutting cards from a full deck should give an ace every 13 times. The mean recurrence time gives the probability of the next eruption in any specific time interval - 1 day, 1 year, 10 years, etc. (see Decker and others, 1995). Decker (personal communication, 1998) clarifies the concept by using a card analogy to construct a graph: have an experimenter cut a full deck of cards once every 1 minute (the time interval is only important for the graph, not the actual cuts); every time an ace is cut, a point is plotted on the graph for the discovered time interval (drawing an ace is analogous to the eruption start); return the ace to the deck, shuffle the deck and draw again; repeat; after about 100 cuts the "mean recurrence time" for drawing an ace should be about 13 minutes. The probability of drawing any ace in the future will be the same on each draw and does not change if the sequence of "failed draws" exceeds the "mean recurrence time". For geologists familiar with floods this concept is similar to flood frequency.

The past eruption patterns of Mauna Loa have been used by Decker and others (1995) to forecast the next eruption of this volcano. Since 1832, volcano watchers have recorded information on the onset, duration, and end of Mauna Loa's eruptions. These data are compiled in Table 1 and are used to determine recurrence time. A closer look at the data may help to refine the forecast for the next eruption. The cumulative number of historic eruptions of Mauna Loa plotted against the onset dates of the 39 eruptions will help us to predict the next eruption. The eruption data do not define a simple linear trend that closely matches the mean recurrence time. The data plot into at least four clusters which define periods with different mean recurrence times. The intervals 1832-1870 and 1880-1950 were interrupted by an interval from 1870-1880 during which eruptions were much more frequent. A dramatic increase in mean recurrence time is obvious for Mauna Loa since 1950. This increase corresponds to two of the four longest recurrence times in Mauna Loa's historical eruption record: 25 years (1950-1975) and 9 years (1975-1984).

Clustering of the data indicates the recurrence time has varied over time and that the mean recurrence time is not representative of some periods in the volcano's history. Significant changes in the recurrence time correspond to major events in Mauna Loa's history and the behavior of nearby Kilauea volcano. In 1868, M7.0 and M8.1 earthquakes occurred on the south flank of Mauna Loa. These events preceded the increase in eruption frequency in 1870 and may have increased the efficiency of the magma supply system. Alternatively, the increase in eruption frequency may reflect a higher magma supply rate to Mauna Loa from the Hawaiian hot spot which possibly induced the large earthquakes. The number of eruptions of Mauna Loa and Kilauea are inversely correlated for the interval 1916 to 1980 (Klein, 1982). When eruptions are numerous at Mauna Loa, Kilauea has fewer eruptions, and vice versa. The dramatic decrease in recurrence time that followed the 1950 Mauna Loa eruption corresponds with an increase in the frequency and volume of eruptions at Kilauea.

Your assignment:

1. Based on the recurrence intervals given in Table 1 calculate the mean recurrence time (in days and years) for eruptions of Mauna Loa.

2. On a graph (you may use Excel or Quattro Pro/Lotus/? (for you PC users ) to do this or use regular graph paper), plot Historical Eruption Event # (on Y axis) vs Year of Eruption (on X axis).

3. Make a dashed line joining the first and last point (eruption # 1 and #39). Calculate the slope of the "line" . This slope should be similar to the number you calculated in question 1.

4. Calculate the mean recurrence time (in days and years) for the following intervals:
1832 to 1870, 1870 to 1880, 1880 to 1950, and 1950 to 1998.

5. Calculate the slope (as you did for question 3 ) for each of these four intervals. Remember once again to use the appropriate eruption numbers to make your dashed lines.

6. a) Based on the mean recurrence time that you calculated in question 1 and 3, and keeping in mind that the last recorded eruption was in 1984, when should Mauna Loa have erupted? b) Give one explanation for why Mauna Loa did not erupt according to your prediction.

7. Based on the mean recurrence time that you calculated in question 4 and 5 for the interval 1950 and 1998, and keeping in mind that the last eruption was in 1984, when can we expect Mauna Loa to erupt?

Answers:
If you use a spreadsheet to calculate your answers, provide a hard copy of your worksheet along with your answers.

1. Mean recurrence time: in days: _______ , in years: ________

2. Attach graph

3. Show calculations and provide your answer.

Slope = __________

4.
Mean recurrence time for 1832 to 1870: in days: _______ , in years: ________
Mean recurrence time for 1870 to 1880: in days: _______ , in years: ________
Mean recurrence time for 1880 to 1950: in days: _______ , in years: ________
Mean recurrence time for 1950 to 1998: in days: _______ , in years: ________

5. Show calculations and provide your answer.

Slope for interval 1832 to 1870 = __________
Slope for interval 1870 to 1880 = __________
Slope for interval 1880 to 1950 = __________
Slope for interval 1950 to 1998 = __________

6a.

6b.

7.