Introduction
During the summer of 1995 and again in 1996 and 1997, an electronic temperature recording device was deployed in the runoff channel of Grotto Geyser.  The resulting electronic log has been correlated with some 112 visual observations to obtain an accurate, reproducible record of the eruptive activity of this major geyser.  The purpose of this ongoing study is twofold: to build a basis for future reference and comparative studies as well as to explore possible relationships between duration of an eruption and interval between eruptions ( a hypothesis strongly supported by all of the subsequent data).

Location of Geyser
Grotto Geyser is the northernmost of the three remarkable large geyserite cone formations to be seen in the Upper Geyser Basin (the other two being Giant and Castle geysers).  It is situated some 600 feet to the north and slightly west of the next large cone formation which is, of course, Giant Geyser on the west bank of the Firehole River.  Grotto Geyser's formation is unmistakable for its large size and multiple openings through which water is thrown during eruptions.  Immediately (some 30 feet) to the north of Grotto is the lower and smaller cone of Rocket Geyser, which often erupts for several minutes in concert with Grotto.

Description of Eruptions
An eruption of Grotto Geyser is preceded by cyclic overflow of Grotto Fountain Geyser, a feature some 200 feet north and slightly east of the Grotto formation.  This cyclic activity (some 10-20 minutes in period.) usually but not always leads to a major eruption (20 to 60 feet in height for 2 to 20 minutes) of Grotto Fountain.  Other less typical but not rare precursors of Grotto eruptions are cyclic play from South Grotto Fountain (a feature some 50 feet south of Grotto Fountain which has a splashing or bursting eruption to a height of approximately ten feet for one to several minutes) and eruptions of the  "Central Vents" (small vents on Grotto's north platform between Grotto's formation and Rocket's formation that erupt to a height of three feet for several minutes).  Typically Grotto begins its eruption 1 to 4 minutes following the start of Grotto Fountain with a very large (unmistakable) surge of water from all the openings.  The highest play is during this initial surge and may be 20 or 30 feet above the top of the cone lasting a few seconds followed by splashing for the remainder of the eruption.  Eruptions are typically 1.5 to 2.5 hours in duration but may be of any length up to 26 hours or so.  Rocco Paperiello coined the term "marathon"  in reference to any Grotto eruption lasting long enough to trigger bursting eruptive activity from Spa Geyser, a deep funnel shaped feature some 160 feet northwest of Grotto Fountain.  The massive outflow of water during a Grotto eruption (several hundred thousand gallons during a 10-20 hour "marathon" eruption) drains to the west and to the east from the platform and flows down several channels into the Firehole River to the east.

Method of Data Collection
For this study, a Hobo XT temperature logger manufactured by Onset Computer Corporation was placed under the boardwalk south of Grotto with the temperature probe tip deployed in the minor runoff channel immediately to the south of the Grotto formation.  Water temperatures at this location typically ranged from  110o  to 135o Fahrenheit during an eruption. The device recorded probe tip temperature once a minute and this data log was downloaded daily.  Eruption start times appeared clearly in the electronic log as marked jumps in probe temperature occurring when the hot runoff water flowed over the probe tip.  Eruption end times were taken (after much visual correlation, as indicated by the starred end times in Tables 1,2, and 3) as being when the probe temperature fell below 110 degrees F.  This corresponded ( within one to five minutes) to the time when overflow from the east side of the platform had decreased from a flood to a trickle.  Note that by this time splashing from the cone had sometimes ceased several minutes previously.

Summary of the Data
Table 1, Table 2 and Table 3 depict all of the data collected during the study showing not only the date, time and duration of every eruption but also indicating visual observations as well (stars).  The 1996 and 1997 data are each a time series with no eruptions missed during the time of our stay in the Park.  The 1995 data is not a time series as a rodent chewed the thermistor probe lead wire causing a four day hiatus in the data record..

Figure 1, Figure 2, Figure 3 and Figure 4 summarize the durations of eruptions for each of the three years and for all three years together.  The frequency distribution of some 210 eruptions is shown in the Figure 4 histogram.  Note the marked skewing of the data with most Grotto eruptions being of 1.5 to 2.5 hours duration while the remaining eruptions had durations ranging up to 26 hours.  Examination of the histograms reveals apparently significant differences in the frequency distributions of eruption durations for each year of the study.  These apparent changes in behavior of the geyser are probably artifacts resulting from the fact that much less data was collected in 1995 and 1996 than in 1997.  That is, when enough eruptions are recorded, the vacant areas on the histograms tend to "fill in."

Figure 5, Figure 6, and Figure 7 are scatterplots of the data showing the strong, nearly linear relationship between IBE (interval between eruptions start-to-start)  and  duration (of eruption included in the IBE) for Grotto Geyser.  IBE's that included Giant eruptions exhibited the greatest deviations from the prediction (see Table 3).  Least squares linear regressions were computed for each year's data and for all three years together and Pearson's correlation coefficients determined in each case.  Table 4 summarizes these findings.

Table 4  Summary of Linear Regressions
D=duration in minutes start-to-end (is part of the IBE)
IBE=interval between eruptions in minutes (start-to-start)

Year                                       Equation of the Regression Line                            Pearson's Correlation Coefficient

1995                                        IBE=161+1.8 D                                                     .99
1996                                        IBE= 212+1.66D                                                   .99
1997                                        IBE=190+1.7D                                                      .99
1995,1996,1997 (together)     IBE=192+1.7D                                                      .99

If the Figure 8 scatterplot (all three years together) is examined closely it may be seen that the relationship is actually slightly nonlinear.  Note that nearly all medium length eruptions fall above the linear regression model (the dark heavy line on Figure 8) and that very long eruptions tend to fall below the line.  This observation leads to a refinement of the mathematical relationship.  That is, a power function of the form  y=axb  where y=IBE and x=duration can generate a curve that fits the medium and long duration data better than does a linear regression.   At this time David Schwarz, another thermal volunteer, pointed out that because most Grotto eruptions are short, the regression is "unfairly" weighted by this mass of data close to one end of the curve.  He suggested that for purposes of prediction a better fitting curve would result if all but three or four of the short  (for this study less than 150 minute) duration/interval data pairs were dropped from the computation of the regression curve.  His regression equation (IBE=8.7D.776) produced by this "statistically questionable" technique does, as illustrated by the graph of that equation (the fine line on Figure 8)  predict IBE's better from medium to long durations than does the linear model.  One report subsequent to this study (08/07/97 @ 13:27, D=26:35, IBE=42:57) indicates that ultra long IBE's may be much more accurately predicted using the power regression model (predited IBE=44:19) than from the linear regression (predicted IBE=48:23).
 Viewing the relationship as a curve provides an explanation of the otherwise apparently significant differences in the slopes  and Y intercepts of the linear regression lines for the three years.   The differences are probably an artifact resulting from the fact that for each year, the maximum duration in that data set (from which regression line slope is largely determined) is different.  That is, the regression lines are each chords intersecting the power curve at the point representing the maximum duration/interval data pair of that year.

Conclusion
The data show a strong relationship between the length of the present eruption (duration) and the elapsed time between eruptions (IBE) at Grotto Geyser. Thus, predicting the start time of the next eruption is a simple matter of timing the duration of the present eruption and applying the regression equation.  In the three summers of the study we have seen no significant changes in the behavior of Grotto Geyser.  It is extremely interesting to note that the several major eruptions and frequent "hot periods" of Giant Geyser during 1997 has evidently had no large or lasting effect on Grotto Geyser.   There has certainly been no general decrease in Grotto activity  nor has there been a significant change in the best fit regression line or curve (probably the best descriptors of activity and the most sensitive indicators of change in activity).

Items for Possible Future Study
1.  Central Vent activity that precedes some Grotto eruptions appeared in our study to have little or no delaying effect on the start of eruption (the actual and predicted IBE's are very similar) .  More data is needed to support or refute the popular theory that Central Vent activity delays a Grotto start.

2.  The relationship between Grotto and Spa begs for a study.

3.  The possible effect of Rocket major and Grotto Fountain eruptions on deviation of  Grotto IBE's from the prediction warrants study.

To these ends we hope to deploy suitable temperature logging devices at Spa, Rocket, and Grotto Fountain runoff channels as well as continuing to monitor Grotto itself.
 

Lew Johns
Jan Johns

jjohns@shol.com
October 29, 1997