THE UNIVERSITY OF MELBOURNE DEPARTMENT OF INFRASTRUCTURE ENGINEERING ENEN20002 Earth Processes for Engineering Semester 1, 2022 Assignment-1: Stochastic Rainfall Modelling Due: 5:00 pm, Friday April 1, 2022 Introduction Risk analysis is critical to the design and management of water supply systems as shortfalls in water availability have substantial impacts on people, agricultural production, industry, public amenities and the environment. In water supply systems reliant on reservoirs, a significant component of risk is associated with variation in reservoir inflows (runoff), which is related to variations in rainfall. An additional risk that is becoming more and more evident are changes in average rainfall and runoff, relative to historic conditions, associated with climate change. It is necessary to build these uncertainties into a risk analysis when assessing the adequacy of a water supply. The first two assignments in Earth Processes for Engineering require you to understand and model some “Earth Processes” to conduct a simplified risk analysis of a water supply system. Workshops 2 – 6 are designed to help you learn and practice skills relevant to these two Assignments. Lectures 5, 6, 14 & 15 also provide key knowledge to enable you to complete these two Assignments. In successfully completing these two assignments you will gain general problem solving and data analysis skills applicable to a wide range of engineering challenges. So think more broadly about the problems you could address with these techniques – variability and uncertainty are a hallmark of many problems that engineers deal with. The general approach to these two assignments involves: 1. developing and testing a daily stochastic rainfall model for the North Esk catchment that can be used to simulate variation in daily rainfall for historical and climate change conditions; 2. developing and testing a daily rainfall-runoff model for the North Esk catchment that can be used to convert climatic forcing (rainfall and potential evapotranspiration) into estimates of runoff; 3. linking the two models together with a reservoir model (supplied to you) to convert runoff (reservoir inflows) into variation in reservoir storage over time; 4. analysing the resultant model outputs to assess the likelihood of water supply system failure (i.e. running out of water) under historic and climate change conditions. All this analysis is undertaken in Excel. The level of analysis is kept reasonably simple here (e.g. a simple rainfall model [much more complicated models exist] and no complicated reservoir management policies such as water restrictions, etc), as we want to concentrate on the general underlying processes rather than getting lost in details. Problem Description Historical daily rainfall data for the North Esk catchment are provided for 1979-2010. Construct a stochastic daily precipitation model to simulate daily rainfall for this catchment. Use a two-state first order Markov chain model to describe the occurrence of rain (wet/dry day) and a gamma distribution to generate rainfall depths on wet days. Workshops 3 and 4 introduce you to the calculations required. This assignment extends that work to include using monthly variable gamma parameter values and you also have more data available to estimate the distribution parameters and transition probabilities. Analysis Place your workings and results in the appropriate Task labelled spreadsheets provided. Task 1: Estimate the daily transition probabilities and gamma distribution parameters ( and ) from the observed data assuming one set of transition probabilities and gamma distribution parameters can describe rainfall occurrence and depth throughout the year (i.e. monthly-constant). Present your monthly-constant stochastic rainfall model. Task 2: Estimate the daily transition probabilities and gamma distribution parameters ( and ) for each month of the year from the observed data (i.e. monthly-varying). Present your monthly-varying stochastic rainfall model. By monthly-varying we mean that the daily transition probabilities and gamma distribution parameters are different for January, February, etc, but that January always has the same values irrespective of which year you consider, as does February, etc. Task 3: Modify the monthly-variable stochastic daily rainfall model from Task 2 for climate change. Present your climate change adjusted monthly-varying stochastic daily rainfall model. To approximate climate change for this assignment you can change the mean rainfall in the Gamma distributions in your model according to the likely climate change scenarios available from http://www.climatechangeinaustralia.gov.au/. o Select Projection Tools | Summary Data Explorer. o Find the appropriate “Sub Cluster” region for this catchment. o Click on the Sub Cluster in the map and download the summary of Rainfall projections for this region (they are in a csv file). Recalculate Gamma distribution and values for climate change using the median change in seasonal rainfall by 2050 for the RCP8.5 emissions scenario and assuming the monthly coefficient of variation (CV) of wet day daily rainfall remains constant (does not change from the observed value) when adjusting the gamma parameters. The median seasonal change can be applied to each month within that season. Reporting Place your reporting in the appropriate Task labelled spreadsheets provided. When reporting, present any comparisons using graphs and or tables as appropriate with accompanying text to guide the reader. Task 1 & Task 2: For each task report on how well your stochastic daily rainfall model represents the characteristics of the observed data. Your assessment should include, but not be limited to, comparisons of the average and variability of daily, monthly and annual rainfall amounts and rain days. Discuss which aspects of model output are similar, or different, to the observations. For Task 2, also discuss whether any aspects of model output have been improved relative to the Task 1 model. Task 3: Describe how you modified your Task 2 model to reflect climate change conditions in 2050 for the RCP8.5 emissions scenario. Discuss which aspects of model output are similar, or different, to the Task 2 model and whether these similarities and differences in model output align with your expectations. Discuss whether your Task 3 model output aligns with your expectations of projected climate change rainfall. Your discussion should include, but not be limited to, comparisons of the average and variability of daily, monthly and annual rainfall amounts and rain days. Submission Requirements Teamwork and Reporting For this assignment exercise, students are to work in groups and refer to the subject web site (LMS) for group allocation. Each group needs to submit one team report as an Excel spreadsheet fully addressing all the points mentioned above. You will find guidance on report writing on the LMS in the assignment area. There is one item to submit: 1. Your spreadsheet containing your data analysis, stochastic rainfall models and discussion of your results to the link on the LMS. The spreadsheet is to be submitted online via the subject web site. Instructions related to LMS submission can be found below. o The spreadsheet you submit must be a renamed copy of the file “Assignment 1 – 2022.xlsx”, which is the file you downloaded from the LMS containing the data and instructions for this Assignment. o The spreadsheet you submit must be a “live” version; this means that values in cells update when other data change. This allows us to mark your workings. Avoid using PasteSpecial as Values as this destroys your workings. You may PasteSpecial as Values random numbers once you are happy with your workings and you don’t want the results to keep changing. o Each group should submit only one spreadsheet using any of the group members LMS user name (don’t submit multiple copies from a group). You must use your workshop time and group name to name your spreadsheet. (e.g. 1:15pm_Group1.xlsx). All the members of a team will need to use the Peer review survey (provided later) to provide feedback on each members’ contribution (including your own) in completing this assignment. This information will be used to assess individual marks from the team report. This assignment is due at 5:00 p.m., Friday April 1, 2022. You need to submit the spreadsheet by that deadline. Late submissions received after the due date without prior arrangement will receive a penalty of 5% per day late. How to submit the spreadsheet on the LMS: On the LMS main menu for the subject you will find “Assignments”. In “Assignments” you will find a page with the title “Assignment #1 – Files & Group Submission”. In this page you should: Submit your spreadsheet to the “Submit Assignment” link.
