Background of the Problem
You are a graduate engineer working for a company that recently completed the design of an open channel for delivering water from the Rainbow Reservoir to the Forrest Dam. The purpose of this channel if to eventually use the water for irrigation. Your previous client, the Little Hill Irrigation Trust is very happy with the work you and your team have completed, which is great as this was your very first time participating in a water engineering project.
Following the channel design project, your company won another project from the local water utility, Little Hill Water Corporation (LHC). The job at hand is to develop a water resource management plan for the Rainbow Reservoir. The reservoir and the Little River catchment have been sketched in in Figure 1. The catchment has an overall area of approximately AC = 160 km2 , the dominant land use is rural. There are a total of 6 rain gauges with rainfall data (Fig 1).
Schematic of the Little River catchment area and the downstream Rainbow Reservoir (not to scale).
Runoff from the catchment flows into the Little River and it is measured at a flow observation station before the water reaches the Rainbow Reservoir. The surface area of the reservoir is AR = 4 km2 . The reservoir can reach a maximum depth of 30 m before inducing overflow through the spillway. The walls of the reservoir are almost vertical, therefore there is little variation in surface area at different depth. The reservoir provides irrigation water to the Forrest Dam via an open channel (already designed), drinking water to the local community via a pipeline, and allows for environmental water deliveries to maintain the natural environment at the downstream of the reservoir.
Your company is impressed by your positive attitude and the quality of your work. As a result, you have successfully passed the probation period, and have been given the opportunity to join the hydrology team to participate in the LHC project.
You are tasked to solve several specific engineering tasks that will contribute to the water resource management plan. Critical steps of the calculations should be documented such that your results can be double checked by your colleagues.
Tasks
Question
1. The first task of the project involves a water balance analysis in the reservoir as correctly quantifying the water balance is an essential part for reservoir management. The water balance in a reservoir means that the change in the water volume on the reservoir (storage) must be equal to the total volume of water coming in (inflow) minus the total volume leaving the reservoir (outflow).
The inflow includes direct precipitation on the reservoir surface area (P) and runoff reaching the reservoir via the Little River stream (Qs). The outflow includes drinking water supplied to the water treatment plant (Qw), irrigation water supplied to the Forrest Dam (Qd), the environmental flow releases (Qe), evaporation to the air (E) and percolation to the ground water system (G).
Currently, there is no record of the evaporation and the percolation, and they need to be estimated.
(i) Records of the reservoir level, precipitation P, stream inflow Qs, drinking water outflow Qw, irrigation water outflow Qd and environmental flow Qe have been supplied by the client. The data for the first four months of 2023 are shown in Table Q1-1. Perform a calculation of the change in water storage volume and combined volume of water evaporated and percolated for each of the first three months (i.e. January, February and March, respectively) by water balance calculations.
(ii) The percolation can be assumed as at a constant rate. The evaporation is dependent on may factors, including the weather condition. The average weather condition in February has been sourced from a local weather station and summarised in Table Q1-2. To further estimate the percolation rate, use the Penman’s method to estimate the evaporation for an average day in February, then use the combined total volume determined in (i) to estimate the percolation rate in ML per day. Wind function can be considered as f(u)=(8.5 + 0.36u) MJ/m2 /kPa/day, when u is in km/day. Demonstrate the key calculation steps and fill in Table Q1-3. Based on these estimates, is the reservoir gaining or loosing water from percolation?
2. The second task involves the calculation of annual precipitation, in particular you are required to determine the long-term average annual areal rainfall for the Little River catchment based on the annual rainfall data provided by the client, as shown in Table Q2-1. As shown in Figure 2, there are four rain gauges (A, C, D, and E) within the area of the Little River catchment area, and another two rain gauges (B and F) outside but not far from the catchment. Rain gauges B and F were replaced at the beginning of 2004 since the instruments were found malfunctioning. This also indicates that the rain data collected at points B and F prior to 2004 may have errors (highlighted in red).
Thiessen polygons for stations A-F in Little River catchment area. (Scale provided)
To determine the long-term average annual areal rainfall for the Little River catchment, the average annual point rainfall at all the rain gauges needs to be determined. However, the records at gauge B and F need to be corrected before a correct average annual areal rainfall can be determined. A senior engineer has suggested the following steps:
(i) Thiessen method is the preferred method for areal rainfall estimation. An aerial map of the catchment has been provided by the client and another colleague has drawn the Thiessen polygons (Fig 2). Determine the areas in km2 for each of the contributing areas from each of the stations. Based on your results, do all stations contribute significantly to the rainfall over the Little River catchment? Can any of the stations be discarded from analysis? If so, how do you correct the Thiessen polygons? Complete Table Q2 – 2 and delete the row for any discarded data
(ii) Following your analysis of contributing areas from Thiessen polygons, use the double mass curve method (also known as the double cumulative curve) to correct the rainfall data at the necessary gauges. Use the average values from gauges A, C, D, and E as the reference data. Demonstrate the steps you take for the calculations and summarise the results in Table Q2-3. Plot the double mass curve for the original data and the corrected data.
(iii) Once the necessary data is corrected, use the Thiessen method to calculate the long-term average annual areal rainfall and complete.
3. The third task is related to predicting the magnitude of a flood. Floods will occur after storm events and they may put pressure on the infrastructure (channels, earthworks, embankments, dam, spillway, gates, etc).
As part of a flood risk analysis, forecasts of flood peaks in the river are necessary. Since it takes time for the runoff from the catchment to converge to the river outlet, there is a delay between the storm peak (rainfall) and the flood peak in the river (typically from hours to days). The flood pattern and peak in the river can be estimated by determining the hydrograph for the storm event. An intensive storm has hit the Little River catchment area. The client worries about the flood risk of this storm, because prior to this storm, the catchment has experienced mild but extended rainfall. It is believed that the soil is saturated, and the infiltration capacity have reached its limit. The river flow has also reached a relatively high but steady baseflow of 350.6 m3 /s prior to this storm.
The client has added an additional task to your project – predicting the hydrograph and the flood peak of this storm event. It is an urgent task, and you are asked to stop what you are doing and to jump to this hydrograph estimation task immediately. It is also an expectation that the results should be delivered to the client ASAP (in hours and on the same day) to maximize the window of preparation.
To facilitate your calculation, the client has provided the S-curve for rainfall excess of 1 unit (1 cm) per hour for the Little River catchment, and it is given in Table Q3-1. The infiltration capacity for the catchment has been calibrated before using the Horton’s equation
4. The fourth task is also related to predicting magnitude of floods, however this task focuses on estimating the risk of flood peaks for future storm events. The flood frequency analysis of the Little River was done more than 10 years ago with limited data. Your client requests an updated analysis of the flood peaks for storm events with 10, 50, 100 and 500 average recurrence intervals (ARI) based on the updated annual peak flow records.
(i) Calculate normal and logarithmic (log10) statistics of the series (Mean, Standard Deviations and Skewness) using Excel.
(ii) Using the frequency factor formula (quantile estimation), estimate the 10, 50, 100 and 500 ARI flood peak considering the data is not inconsistent with (a) Log-Normal distribution, (b) Log Pearson type III distribution, and (c) Gumbel distribution. Upload the Excel spreadsheet for the calculations such that your colleagues and the client can verify your results.
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