1 Outline of practical In this practical we will simulate river flow and estimate the prob ability of a flood 2 Background 2.1 River flow equations The flow in rivers is commonly measured from a weir. For a sharp crested rectangular weir the flow Q (metres second) is calculated from the height of the water surface above the weir H (metres), the weir discharge coefficient K, the length of the weir seras the river L (metres) according to Q = K2 where and g is the acceleration due to gravity. A hydrologist considers that Lisa known constant, but that is uncertain and that is subject to measurement error. 222 Parameters For the given weir, we know that the length of the weir is 10 metres, the weir discharge coefficient is 0.7, and the measured height is 1 metre Waterflow function Write a function of the form function - calculate_river_flow(L, K, H) end that takes the values L: length of weir, K: weir discharge coefficient, and H: height of water surface over weir - may be vector. You can check your function in MATLAB GRADER - see link in Canvas 4 Predicting mean river water flow We know that the height is randomly distributed and can be mod- elled with an exponential distribution with a rate of 0.5. Remember to set your seed 1. Simulate a year's worth of daily heights for consistent results 2. Hence, calculate a year's worth daily river flows 3. Calculate the expected mean daily river flow. 4 Predicting mean river water flow We know that the height is randomly distributed and can be mod- elled with an exponential distribution with a rate of 0.5. Remember to set your seed 1. Simulate a year's worth of daily heights for consistent results 2. Hence, calculate a year's worth daily river flows. 3. Calculate the expected mean daily river flow. For this section, you will need to write a script and submit it to MATLAB CRADER A template to ensure that it works fine is given below, this is also on MATLAB GRADER - see link in canvas. Set up parameters L- III 5 . We will stalate one years worth of data mng(2020) 2 set sees to repeatable. Nezt we calculate the associated river water slous. 1 - calculate_river_flow (L, K, 1); z Calestate meas river flow mean_flow-: X Catestate prob of flood prob_flood - > function - calculate_river_flow(L, K, H) Note that to make your function easily accessible from the script, we put it at the end of the script 5 Predicting the probability of flooding We are told that flooding will occur if the river water flow is greater than 100 metres second 1. Using your simulated data, calculate the probability of flood- ing in a given year. Again, please add this to your script and check in MATLAN GRADER. 6 Submission Submit your function calculate_river_flow() and simulation script to MATLAB Grader on MyUni to receive credit for complet ing this practical 1 Outline of practical In this practical we will simulate river flow and estimate the prob ability of a flood 2 Background 2.1 River flow equations The flow in rivers is commonly measured from a weir. For a sharp crested rectangular weir the flow Q (metres second) is calculated from the height of the water surface above the weir H (metres), the weir discharge coefficient K, the length of the weir seras the river L (metres) according to Q = K2 where and g is the acceleration due to gravity. A hydrologist considers that Lisa known constant, but that is uncertain and that is subject to measurement error. 222 Parameters For the given weir, we know that the length of the weir is 10 metres, the weir discharge coefficient is 0.7, and the measured height is 1 metre Waterflow function Write a function of the form function - calculate_river_flow(L, K, H) end that takes the values L: length of weir, K: weir discharge coefficient, and H: height of water surface over weir - may be vector. You can check your function in MATLAB GRADER - see link in Canvas 4 Predicting mean river water flow We know that the height is randomly distributed and can be mod- elled with an exponential distribution with a rate of 0.5. Remember to set your seed 1. Simulate a year's worth of daily heights for consistent results 2. Hence, calculate a year's worth daily river flows 3. Calculate the expected mean daily river flow. 4 Predicting mean river water flow We know that the height is randomly distributed and can be mod- elled with an exponential distribution with a rate of 0.5. Remember to set your seed 1. Simulate a year's worth of daily heights for consistent results 2. Hence, calculate a year's worth daily river flows. 3. Calculate the expected mean daily river flow. For this section, you will need to write a script and submit it to MATLAB CRADER A template to ensure that it works fine is given below, this is also on MATLAB GRADER - see link in canvas. Set up parameters L- III 5 . We will stalate one years worth of data mng(2020) 2 set sees to repeatable. Nezt we calculate the associated river water slous. 1 - calculate_river_flow (L, K, 1); z Calestate meas river flow mean_flow-: X Catestate prob of flood prob_flood - > function - calculate_river_flow(L, K, H) Note that to make your function easily accessible from the script, we put it at the end of the script 5 Predicting the probability of flooding We are told that flooding will occur if the river water flow is greater than 100 metres second 1. Using your simulated data, calculate the probability of flood- ing in a given year. Again, please add this to your script and check in MATLAN GRADER. 6 Submission Submit your function calculate_river_flow() and simulation script to MATLAB Grader on MyUni to receive credit for complet ing this practical