We have data from 10 different infiltration measurements, and the spreadsheets for each of these are numbered from 1 to 10. Theory and experience both suggest that there will be some variability in space, and also that there can be some variability due to measurement procedures (e.g., the size of the infiltration rings, the use of a single ring vs. a double ring, the depth of ponding, the accuracy of the volumes added per unit time, and the precision of the measurements, and whether the measurements stabilized at some point “asymptotic infiltration rate”).
Trang 1Group6 6 May 2017
Student name:
Infiltration and Hydraulic Conductivity
We have data from 10 different infiltration measurements, and the spreadsheets for each of these are numbered from 1 to 10 Theory and experience both suggest that there will
be some variability in space, and also that there can be some variability due to measurement procedures (e.g., the size of the infiltration rings, the use of a single ring vs a double ring, the depth of ponding, the accuracy of the volumes added per unit time, and the precision of the measurements, and whether the measurements stabilized at some point [“asymptotic
infiltration rate”])
Another characteristic of these data sets is the short-term variability in the amount of water that was recorded as infiltrating from minute to minute Some of this short-term
variability may be due to the relatively crude method used for maintaining constant water levels, but there also may be variability due to the wetting front reaching a macropore, gravel layer, root hole, or some other unknown soil factor The point is that field data usually don’t look nearly as nice as most textbooks show The messiness of real data means that one often has to use averages, professional judgment, or other techniques to come up with a best
estimate of the final infiltration rate
Infiltration Data
1 The logical first step in our data analysis is to estimate the final infiltration rate from each of
the infiltration experiments Please make a table listing the infiltration tests that you were assigned to use in this assignment in order of decreasing ring diameter (i.e., 15 cm, 20 cm, etc.) For each of these six tests list: (i) your estimated final infiltration rate in cubic
centimeters per minute; (ii) the area of each ring; and (iii) your estimated final infiltration rate
in centimeters of water per unit area per hour as indicated below Use the appropriate number
of significant figures as indicated by your handout and lecture materials
Trang 2Group Diameter
(cm)
Asymptotic infiltration (ml/min)
Area (cm² ) Asymptotic
infiltration (cm/hr)
2 The large amount of temporal variability (variation between minutes) makes it difficult to
accurately estimate the asymptotic (final) infiltration rate To help estimate the asymptotic infiltration rate it is helpful to “smooth” the data For data collected over time the most common smoothing technique is a moving average, and this is described below
The basic idea is that you choose how many data points you want to average (“n”) You then take that number of data points, starting at the first point, add them up, and then divide by n You then subtract the first value in the time period, and add in the next (n+1)
data point, and again divide by n As an example, imagine a time series of annual values that
is 22 in year 1, 20 in year 2, 24 in year 3, 30 in year 4, followed by 20, 26, 16, 18, and 20 in year 9 If you decide to you a 3-year moving average, the first value would be 22 for year 2 (22+20+24 divided by 3), and then 25 for year 3 (subtract 22 as the value for year 1 and add
30 as this is the value for year 4) The subsequent values would be 25, 26, 21, 21, and 18 (for year 8) Note that a five-year moving average for ten years of data would yield only six plottable points because you cannot calculate a moving average for years 1 and 2, or for years
9 and 10
You should recognize that an increase in n (i.e., the number of data points in the moving average) will increase the amount of smoothing and hide more of the short-term variability In contrast, a smaller n will reduce the amount of smoothing (i.e., increases the
variability over time) and allows any one data points to have a greater effect on the moving average Compare, for example, the smoothing from a 10-year moving average to the
smoothing you might expect from a 3-year moving average A moving average is often applied to hydrologic data such as annual precipitation, and you should be able to visualize how a moving average can help identify trends The trade-off is that a moving average will hide the more extreme values and the short-term variability You can write a simple macro to calculate a moving average, or you can use the moving average function in excel The second smoothing technique is to simple average all of the short-term data over some longer time interval In other words, five one-minute readings could be aggregated (averaged) to get one value to represent a five-minute period You then do this for each five minute period to more easily see the longer-term trends Like a moving average, this averaging procedure will
Trang 3reduce the short-term variability, and the trade-off is that you: 1) lose information on the short-term variability, and 2) reduce your sample size
To illustrate these techniques you will work with the data set identified with an asterisk
in the table on page 1 Note that you could do exactly the same technique with each of the other data sets, and each data set might yield somewhat different results A table with the suggested column headings is provided at the end of this question in order to help you better understand what you have to submit for this portion of the assignment
(a) Tabulate the time and volume of water added for each minute in columns 1 and 2 In a third
column calculate the 3-minute moving average, and continue this until you run out of data In
a fourth column indicate the midpoint of the time interval corresponding to each data point for your 3-minute moving average Note that the first data point at 1.0 minutes actually
represents the infiltration rate from 0.0 to 1.0 minute, so the midpoint of this time period for plotting is 0.5 minutes, NOT 1.0 minute Hence the midpoint of the times associated with each data point, and the point that should be used for plotting the data, are different from the times listed on the data sheet This means that the first three-minute interval extends from 0.0
to 3.0 minutes, and the true midpoint of this first 3-minute interval is at 1.5 minutes The midpoints of the time represented by each data point are important, as these are necessary to accurately plot the data
(b) Beginning with the first data point, , calculate the eight-minute moving average until you run
out of data (note you cannot calculate an 8-minute moving average if you have less than eight data points, so the eight-minute moving average will have to stop short of the last data point
at minute 65 or 70 Again construct a second column to show the midpoint of each interval
(c) Beginning with the first data point, aggregate (sum) the 1-minute data by eight-minute
intervals (1 to 8 minutes inclusive, 9 to 16 minutes inclusive, etc.) Set up a second column where you divide the aggregated data by eight to obtain the average rate for each eight-minute interval in cubic centimeters per minute Finally, set up a third column to indicate the
midpoint of each time period associated with each of the 8-minute averages Note that you will not have any more than about eight data points, depending on the length of you’re the dataset you are using
You have now completed the calculations necessary to accurately plot the measured infiltration data using three different smoothing techniques (3-minute moving average,
8minute moving average, and 8-minute averages) Such plots are useful for seeing the larger trends in the data In this case, making these plots could help you to better estimate the asymptotic infiltration rate (most people can assess trends much more easily from smoothed data than from a scatterplot or a table) However, for this assignment I’m not requiring you to plot the original data, the moving averages, or the aggregated data as the assignment is already long enough! Nevertheless, you need to at least carefully look at the data in your spreadsheet and compare the asymptotic infiltration rates that you would estimate from the 3minute moving average, the 8-minute moving average, and the 8-minute aggregated data,
respectively If you have trouble visualizing the data, you may want to create quick plots of the data so you can compare the different smoothing techniques against each other and the original 1-minute data
(d) After looking at your values, (i) state which smoothing technique best represents the data; and
(ii) briefly justify your answer
Trang 4(min)
Volume
(mL) 3-minute moving
average (mL/min )
Midpoin
t for each data point (min)
8-minute moving average (mL/min )
Midpoin
t for each data point (min)
8-minute averages (mL/min )
Midpoin
t for each data point (min)
In my opinion, I think that '3-minutes moving average' is better than '8-minutes moving
average' Because we can see that, when we applied '3-minutes moving average' technique,
we can get the results that similar with real results( result of experiments)
3.
When the ring diameter increased from 314cm² to 1804.64 cm² and look at the chart, the permeability increased from 61.14649682 cm / hr to 145.9660297 cm / hr
We see in this chart tends to increase the diameter of the permeability increase
Area (cm²) infiltration (cm/hr)Asymptotic
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Using the results from questions 1-3:
1 From the result of 7 groups were shown in question 1, the average infiltration rate of study site was estimated by:
( ml/min)
Convert to : 136.8345836 cm/hr we can not use this method for evaluate the infiltration rate of study site
Discussion about the results from separate group with different size of ring, with different
of ring size which ratio with infiltration rate when size of ring increasing, the infiltration rate also increased With different of size, site and elevations It was very difficult to estimate
“true” result for study site We can not compare with each other So from question 3, we think that with a big ring we can archive better results We estimated by average method was not good for totally in evaluate the infiltration rate But in my opinion, I thinks that the ratio of diameter is 25-30cm is more stability
In sort of that, we decided to estimate that with diameter of ring equal to 30cm, the
infiltration rate was more better is 1440ml/min or 118.9 cm/hr
2 In my knowledge that the most key factor impacts on infiltration rate which measured is diameter of rings We can see the quite different from those results which measured by private groups, that is practical aspect Another aspects, I think that soil types and texture of soil are also a key factors impacts on it Because of with different site with another elevation which I mentioned, the infiltration rate can be affected strongly An addition, in process of
measurement and analyze the results , may students can be missed understand or come wrong with data which archived from study site In theoretical , I think that some factors from natural conditions such as temperature, moisture in soil can be affected to results Because of with drier soils, it need more water and vice versa with wet soil, and also higher temperature impacts on evapotranspiration of vapor water in odd water
5 The distance between group 1 and group 6 is 5 meters The distance between group6 and
group 2 is 2 meters The distance between group 3 and group 6 is 3 meters The distance between group 4 and group 6 is 4 meters The distance between group 5 and group 6 is 1.5 meters The distance between group 6 and group 7 is 7 meters
Gradient of the error of the group will be different because of different seat measurement 1m is estimated 1% of different, 15m is estimated about 10% of different, 100m is estimated 100% of different