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ENEN20002 Earth Processes for Engineering

创建日期：2024-04-29 17:49:44

所属分类：土木工程civil engineering

标签： ENEN20002

Earth Processes for Engineering

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DEPARTMENT OF INFRASTRUCTURE ENGINEERING
ENEN20002 Earth Processes for Engineering

Assignment-1: Stochastic Rainfall Modelling
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.

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