Reference no: EM132397576

CIV3204: Engineering investigation - Monash University Australia

ASSIGNMENT

The assignment for this subject consists of the analysis of streamflow and rainfall data for the Woori Yallock catchment in Victoria

For each part of the assignment, your report should outline how you performed the calculations, and the steps you took to come to your conclusions.

2.1 Data Analysis

First, use three sets of five consecutive years (for example 1976 through 1980), making sure the three sets do not overlap. Table 2.1 lists the years to analyze depending on your student ID number. These sets of years are roughly covering the beginning, middle, and end of the time series, respectively. Calculate the mean, standard deviation, and skewness for the streamflow each of the three sets. Calculate the same statistics for one year in each of the three sets. Comparing the one year to the five year statistics, are there any conclusions you can draw?

2.2 Probability and Distribution Fitting

For the same data sets as in the first part of the assignment, we will check whether or not the streamflow data follow a lognormal distribution (in other words, if the logarithms of the data follow a Gaussian distribution). We will apply a χ² test for this purpose, with 5% significance.

What conclusions can you draw from this analysis?

We will also test the Gaussianity of the logarithms of the flows through a Gaussian probability plot, as explained in slides 29 and 30 in week 4. Table 2.2 shows the year that you must analyze, depending on your student id number. What do you conclude from this analysis?

Through a routine water quality analysis, it is found that somebody has illegally dumped paint in the river. This paint has been found downstream of an area with 50 houses. This means that any of these 50 houses could have polluted the water. Through analyzing the houses, a consultant has determined that there is an 90% chance that the paint used by household A is the paint that is found in the water. Does this mean that there is an 90% chance that household A is guilty of polluting the stream? If yes, explain your reasoning. If not, calculate the chance that the household is guilty, and explain your reasoning.

The council decides to perform a water quality check every day. This test costs $500 each day. If a pollutant is found in the water, they assume that they will find the pollutor, and they will fine them $50,000. What does the probability to find a pollutant in the sample each day at least have to be, for the council to be 90% sure that they will not lose money on these tests, in a non-leap year?

The council is contemplating organizing nature walks along the river with a paid guide. The walks last for a day, and the guide charges $50 per customer per day. The salary of the guide is $1100 per week, and he is expected to guide at least 25 people per week. How certain can the council be that they will be cash-flow positive any random week?

2.3 Sampling Distributions

Table 2.3 lists the year to analyze depending on your student ID number. From the data in that year, take a sample of 100 random discharge observations (with replacement) and calculate the mean. Repeat this 100 times. Plot the distribution of these sample means, and compare to the theoretical sampling distribution. Do the same exercise with 200 and 1000 repetitions. What can you conclude about the obtained distributions?

Assume you have one day with 24 observations. What is the probability that the daily average is going to be larger than 0.5, 1, 2 and 3 m³s⁻¹?

We want to check whether or not the annual averaged streamflow has changed over the years. We will use an ANOVA for this purpose. We will work with annual averages of the streamflow data. The years 1970-1979 are assumed treatment 1, the years 1980-1989 treatment 2, the years 1990-1999 treatment 3, and the years 2000-2009 treatment 4. Check at the 5 and 10% significance levels if the averages for the four decades are different or not. If there are differences, use the Tukey-Kramer procedure to check which decades are different from each other.

We also want to test whether the variability of the time series has changed over the years. Pick a random year in the first five years of the time series, and another in the last five years of the time series. Check if there is a difference at the 5% significance level. Does this change at the 1% significance level?

2.4 Linear Regressions

For all years from 1969 through 2018, calculate the annual total streamflow and rainfall. As the rainfall data are daily, the total (in mm) can simply be calculated by summing all measurements in the year. For the streamflow, the measurements do not have the same time step, so the total can be calculated as:

Q_tot = Σ^N_i=2 Δt_i−1,i ((Q_i + Q_i−1)/ 2)                 .........(2.1)

N is the number of observations in the year, Q_tot is the total discharge in m3, Q the discharge observation (m³s⁻¹), i the time step number, and Δt_i−1,i the amount of seconds between measurements i − 1 and i.

Also determine the highest rainfall and streamflow values for each of these years. Plot the annual rainfall volume as a function of time. Perform a linear regression, and check if the slope and correlation are significant at the 95% confidence level. Also check if there is autocorrelation in the data, at the same confidence level. Perform the same analysis for the rainfall annual highest peak. And then also perform this analysis for the streamflow. What conclusions can you draw from this analysis?

Also plot the annual streamflow volume as a function of the annual rainfall volume, and perform a linear regression. Check if the correlation is significant, again with 95% confidence. Perform the same analysis for the rainfall and streamflow annual peaks. Which conclusions can you draw? Plot the annual rainfall volume as a function of the annual streamflow volume, and perform the linear regression. Invert the regression line (thus, rewrite the equation as Q_reg = I + S ∗ P_reg). Using the regression equations, write the inverted slope and intercept as a function of the slope and intercept of the slope and intercept of the original streamflow as function of rainfall-regression, and the parameters (means, correlation coefficient, slopes, etc.) of this regression.

Perform a time series analysis on the streamflow data for the year listed in Table 2.4. Take the following steps:

• For each day in the year, calculate the average streamflow. So you will have a time series of 365 (or 366) values.

• Check if the AR(2) model is valid (see page 33 on the slides for week 11).

• If it is valid, calculate the parameters of the model.

• Generate 10 time series of length 1000, and 10 time series of length 10,000.

• For the generated time series, compare the autocorrelation of lag 1, 2, the mean, and the standard deviation to the values of the original time series. Are there any conclusions you can draw?

Attachment:- Assignment Details.rar