INSTRUCTIONS FOR LAB 3

INTRODUCTION:

 
There are many ways to calculate the integral value of some expression, including mathematical, computer-aided, and pencil-and-paper methods.  We will be using a computer-aided method with EXCEL, and a pencil-and-paper method.  This portion of Lab 3 will help you to calculate the value of the denominator of the equation below:
where Q is the discharge, Ct is the initial tracer concentration, Cb is the background concentration of the tracer in the stream, Vt is the volume of tracer added to the stream, and Cd(t) is the tracer concentration measured at the downstream site over time.  By examining the physical meaning of the integral of conductivity over time, we know that value of the denominator in the above equation can be derived from area that is bounded by the conductivity curve on a conductivity-time graph, where the downstream concentration, Cd, is plotted on the y-axis, verses time on the x-axis.  So, the problem is how to compute the area under the conductivity curve.


PENCIL-AND-PAPER METHOD:

Engineering Paper:

The paper that you will be using for this exercise is often used by engineers and is called engineering paper.  Engineering paper is grided every 2 millimeter in both the longitudinal and the latitudinal directions.  Every 10 millimeters the lines become thicker to make them more easily recognizable.

Graphing:

1)  Calculate the maximum values on the x- and y-axis and figure out the scales to use for your graph.  A graph with approximately of 20 cm in width and 15 cm in height is appropriate.  For this exercise we recommend that you set up your graph so that 1 grid represents 4 seconds on x-axis and 1 uS/cm (unit of conductivity) on y-axis. For this scale you will need to multiply the number of smallest squares by 4 to get the area under the curve.
2)  Label and number the x- and y-axes on the centimeter grided lines.  The x-axis starts at 0 and every 5 grids (1 cm) represent 20 seconds.  Number every 10th grid.  The y-axis may not start at 0.  Because of this you need to select an integer number that is less than your background conductivity.  Number every 5th grid on the y-axis.
3)  Plot  each pair of data (conductivity verses cumulative time) and mark them using a small dot on your graph.
4)  Once you have plotted all your data points, draw a smooth curve through all of them.  The finer this line is, the easier it is to count squares.
Counting:
1)  Outline the edge, or somehow mark those squares which fall completely within the curve.  Count these up and multiply the total number of whole big squares by 25 (there are 25 small squares in each big square and you are interested in the number of small squares).
2)  In some organized manner (i.e. left to right) count up all the small squares that have not been counted yet.  If a square is cut by the curve, estimate what percentage to include in your count.  Keep track of the number of squares you have counted by writing the corresponding total in each area you have counted.

3)  Make sure you do not include the area that corresponds to the background conductivity.  You can add up all the squares that correspond to the background conductivity and then subtract the total number of squares.

3)  To get the area under the curve, multiply the total number of small squares that corresponds to the area of the conductivity curve by 4.  this is the denominator of the equation above!  You can now calculate the discharge of Boulder Creek.

EXCEL BASED METHOD
 
Step 1: Field Data Processing
1)  Enter the data from your filed notes into an EXCEL spreadsheet.  Your data should be arranged in columns: column A should be Field Measurement Number; column B, Time Interval in seconds; column C, Cumulative Time in seconds; and column D, Conductivity in uS/cm.  The second row of each column should include the appropriate units, and your data will begin in the third row.
2)  Save your file!
3)  Change this sheet name (not file name) to field. You may use a few sheets today under the same file.  To change the sheet name, position your cursor on the name tab of the sheet at the bottom of the page (it probably says "Sheet1").  Rename this by right-clicking and selecting rename, or by double clicking and typing in a new name.
Step 2: Calculating the Area
1)  Copy all of the field sheet to Sheet2 (not another file):
2)  Calculate the area:  Note:  This is almost the same procedure used in Lab 2 to calculate the areas of each vertical along your cross-section.
Step 3: Graphing
 
You will not need this graph to interpolate your data for this lab, but you need to understand how to plot a graph using EXCEL.  You will be turning in this graph with this assignment.
1)  Highlight data in the conductivity column of the field sheet.
2)  Select the Insert Chart Icon from the menu bar at the top of your screen.
3)  >From the XY-scatter chart menu, select the chart type with a smooth line and data points, and then select the Next button at the bottom of the dialogue box.

4)  Fill in the Chart Title option with your_name.

5)  Fill in the x-axis with Time (seconds), and the y-axis with Conductivity (uS/cm).

6)  In the Chart Location dialogue box choose as object in Sheet3.

7)  Click on the Finnish button.

Now, you may wish to make some changes to this chart, but before you do you need to know:
8)  To re-size or reshape your chart:
8)  To move your chart:
There are many other things you can do to your graph using the menu and options available.  See what you can come up with!