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Use the water quality monitoring data from Heidelberg University (Chapter 2, Exercise 4) to

• plot TP (total phosphorus) against sampling dates to visualize the changes of TP over time and compare the temporal pattern of SRP to that of river discharge (flow). Describe the seasonal patterns in both.

• plot TP against flow, both in the original and log scales to examine the correlation between TP and flow.

Chapter 2, Exercise 4

The Heidelberg University in Tiffin, Ohio, U.S.A., maintains a long-term monitoring program of several Lake Erie tributaries. The water quality and flow data from the Maumee River station near Waterville, Ohio, can be found at http://www.heidelberg.edu/sites/default/files/ dsmith/files/MaumeeData.xlsx.

(a) Convert the date column into R dates.

(b) Summarize flow and total phosphorus by year and by month.

(c) Plot flow and TP over time.

 
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In addition to NOAA-GLERL, several other institutions also have routine monitoring programs on Lake Erie. Data file LakeErie2.csv contains TP and chla concentration data collected by NOAA-GLERL, Ohio Department of Natural Resources (ODNR), and The University of Toledo (Toledo).

(a) Compare the distribution of the TP concentration data from NOAA to the same from ODNR:

• Are the two distributions different?

• If so, is the difference between the two TP concentration distributions more likely to be additive or multiplicative?

• Are the variances of the two distributions the same?

(b) Describe the difference in the two distributions in non-technical terms.

(c) Repeat the previous comparison to compare TP distributions from Toledo and NOAA, and ODNR and Toledo, and summarize the results.

 
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The Great Lakes Environmental Research Laboratory of the U.S. National Oceanic and Atmospheric Administration (NOAA-GLERL) routinely monitors the western basin of Lake Erie from May to October every year. The data file LakeErie1.csv includes all available data up to the end of 2014. Two variables are of particular interest in studying lake eutrophication. They are the total phosphorus (TP) and chlorophyll a (chla) concentrations. These are concentration variables and we often assume that their distributions are approximately normal.

• Read the data into R and use the graphics to evaluate whether TP and chla are normally distributed.

• Western Lake Erie’s nutrient concentrations are largely associated with Maumee River input, which varies from year to year due to variation in weather conditions. As a result, we expect that TP, as well as chla, concentration distributions vary by year. Use the function qqmath (from package lattice) to draw normal Q-Q plots of TP and chla concentrations by year. Are the annual concentration distributions closer to being normal?

 
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Carl Sagan’s intelligence data. In his book, The Dragons of Eden, Carl Sagan presented a graph showing the brain and body masses, both on log scale, of a collection of animal species. The purpose of the graph was to describe an intelligence scale: the ratio of the average brain weight over the average body weight to the power of 2/3.

(a) Read the data (in file Intelligence.csv) into R and graph brain weight against body weight, both in logarithmic scales. The brain weight is in grams and body weight is in kilograms. Can you tell which species has the highest intelligence from this figure?

(b) Calculate the intelligence measure (call it Int) and add the result as a new column to the data frame.

(c) Use the function dotplot from package lattice to plot the intelligence measure directly: dotplot (Species~Int, data=Intelligence)

(d) The dot plot orders the species alphabetically. Reorder the column based on the intelligence scale using function ordered and redraw the dot plot so that the species are sorted based on their intelligence scales. Is there a problem in the data? If so, what might be the cause of the problem?

 
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