Examples of how it is useful:

• Baseline drift in an analytical method.  This may result from wear on the tubing in a pump, from aging of the reagents, etc. You may be able to recognize the problem by visual inspection, but statistical tools may help.
• Climatic cycles.  What is really happening for global warming?
• Business trends.  This goes beyond the stock market.  An industry that fails (e.g., electric typewriters) can shift populations and change both the industrial loads and the municipal loads for waste treatment.

identify type of behavior and recognize magnitudes, time intervals, and regularity.

Special considerations for hydrology:

• Events are interlinked.
• Run off is of great interest to environmental engineer, but this is much more complicated than just the input of rain.  The current levels of streams and impoundments are major factors for what happens to their levels when there is rain.  Furthermore, ground water levels are changing.  A downpour when the ground water is very low may have little effect on run off, but a light rain when the streams are high and the ground is soaked may cause a flood.

• easy to use common random number generator, but this is a highly incorrect distribution.
• better to use randomized normal distribution, but rainfall may not be distributed normally

Testimonial by an environmental engineering student

From: "Nathan Carl Florio" <florin@rpi.edu> Date: Tue, 9 Dec 1997 14:23:18 -0500

 Last week's topic of time series analysis is a very familiar one to many environmental engineering students like, yours truly. We deal with this often in a class we are all taking right now called "Introduction to Applied Hydrology". There have been many times this semester for which we were required to use weighted averages, find the regularity of a system, and the magnitude of the system itself.

As a matter of fact, in the past week or two in that class we were required to do a final project for the course. Almost all of us needed to use time intervals and weighted averages to do a runoff computation for these calculations. We had to realize that the ground water levels effects this runoff just as much as the amount of rain fall or that has fallen. As the ground water level increases so will the surface runoff, while if the ground is not saturated there will be little so no runoff whatsoever.

To do this we can begin by looking at a rainfall graph with a moving average much like the Temperature graph which we viewed on the Environmental Systems Web page. From a graph like this we can see patterns in rainfall, which had many different uses. One of the most common uses of this (combined with the probability and statistical tools we learned earlier) is to design this such as detention basins, treatment plants, etc. etc. We do this to a probability year storm (e.g. 50-year storm), however this analysis can not be done without data to compute these numbers. This data is a time interval with a moving average.

Another use of the time series is in modeling. I believe that we also were required to use this in one of our past courses called "Modeling and Analysis of Uncertainties". Many times in this class we need to use a random number generator (such as on Excel) to compute a model of a system. This is a a quite accurate way to model because a human could not get this kind of variation from their own calculations and hypotheses.

This week was a good reminder of how useful the time series can be and also a nice review of the basics of this analysis. The homework assignment using the basic program was one of the more interesting of the past few weeks and I executed many runs of the program because I was quite curious to find the outcome.

Thank you,
Nate Florio