Class Project Presentation: "Predicting the Level of Lake Huron"

This website explores possible explanations and relationships of water

level fluctuations of Lake Huron which lies between the United States

and Canada. It also includes Lake Michigan because the two lakes are

joined near Mackinac Island. The common level of these very large

lakes is more like an ocean than a river or typical lake because they

do not seem to be related to the amount of rain. The lake level can only

change about a foot over a period of many months. There are short term

fluctuations of up to 10-feet or more due to high wind and waves but

these average to zero when the weather returns to calm conditions.

The basic R program is distributed with three standard datasets that we

use to analyze and predict the level of Lake Huron. We use the following

datasets for our analysis.

• LakeHuron - Annual Lake Levels starting in 1875
• sunspot.month - Monthly sunspot count starting in 1749
• nhtemp - Annual temperatures in New Haven, CT from 1912-1971

Processed Raw Data

    year running_2_year_temp running_2_year_spots weather Huron_Lake_Level
166 1914            50.53333              58.5000 not hot           578.92
167 1915            50.93333             233.6000 not hot           578.09
168 1916            49.96667             456.1000 not hot           579.37
169 1917            49.46667             833.3000 not hot           580.13
170 1918            49.03333             966.1333 not hot           580.14
171 1919            49.53333             992.3000 not hot           579.51

In order to expore the level fluctuations of Lake Huron, we built a

regression model using the lm function in an attempt to predict the lake

level from the three-year running temperature and sunspot counts. Our

model includes an interactive term data frame for joint sunspot-

temperature interaction.

Conditioning Effect of Temperature and Sunspot Level

The model is based on temperature dependance with adjustment for sunspot

level. The sunspot level is represented as a binary high or low

variable. Red dots in Figure-2 below represent high sunspot years when

the level was higher than the 75th percentile which corresponded

1075 sunspots per year. Black dots indicate average and sunspot levels

below 1075. The limit of 1075 sunspots that defines high and low sunspot

years can be adjusted using a slider on the interactive website.

Conditioning Effect of Sunspot Factor

High lake levels coincided with high sunspot counts for both high and

low temperatures. The lake level was about average for sunspot levels

greater than the 75th percentile. Low lake levels only occurred when

sunspot counts were low. The red line in Figure-2 is the best fit line

for high sunspot years when the level was higher than the 75th

percentile which corresponded 1075 sunspots per year. The black line is

the best fit line for average and lower sunspot levels. The limit of

1075 sunspots that defines high and low sunspot years can be adjusted

using the interactive website tool.

The highest sunspot levels corresponded to above average temperatures and high lake levels.

To see the effect of the highest sunspot counts of 1375 or more, the slider can be adjusted

to a higher level. The red line in Figure-2 indicates the expected lake level increases

with temperature. High lake levels coincided with high sunspot counts for both high and low

temperatures. The lake level was about average for sunspot levels greater than the 75th

percentile. Low lake levels only occurred when sunspot count was low.

More Study is Required

These results are inclusive and there is obvious missing data. The effects of sunspots and

and temperature conflict in certain cases and the reason is unknown. It should be possible

to study more data in the future to better understand the processes that affect the lake

level.