代写maltal Quantitative Environmental Modelling 程序

日期：2018-05-16 01:32

ENEN90031Quantitative Environmental Modelling

Introduction

This assignment concentrates on the use of global model analysis techniques that can be applied to optimisation, sensitivity analysis and model uncertainty analysis. The final step involves applying your model results to a hydroelectric power scheme to estimate its reliability in meeting demand now and under climate change. The key parts of the assignment are:

1 Global optimisation of your model using Shuffled Complex Evolution;

2 Regional sensitivity analysis to understand the effects of different parameters on the model predictions;

3 Uncertainty analysis using GLUE; and

4 Assessing the reliability of the hydroelectric power plant.

The assessment for this assignment is as follows.

? Model calibration (section 1): (Technical 10%, Discussion 10%)

? Regional sensitivity analysis (section 2) (Technical 10%, Discussion 10%)

? Parameter uncertainty analysis (section 3) (Technical 10%, Discussion 10%)

? Power plant assessment (section 4) (Technical 10%, Discussion 10%)

? Discussion and conclusions (Discussion 10%)

? Quality of report presentation 10%

Your report should contain the following: aims, introduction, results and discussion, conclusions, references and an appendix containing your MATLAB code. The report must be no more than 12 pages (including graphs but excluding the appendix) and any additional pages will not be assessed. In writing your report, try to demonstrate to the reader your knowledge of the methodologies and their limitation using academic references and modelling results. Please submit your report using the LMS TurnItIn link.

Engineering Practice Hurdle

This assignment can be used as the final piece of your Engineering Practice Hurdle Written Communication submission. STEP workshops and online lessons are available to help you further develop your writing skills. See the Skills Towards Employment Program community

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(COM_00631) for more details on the Engineering Practice Hurdle.

Time Periods

Please use 1980-2006 for parts 1-3 of the assignment.

Please use 1951-2010 for part 4 of the assignment.

1 Global Calibration using Shuffled Complex Evolution (SCE)

Using the SCE algorithm, the model parameters can be adjusted to best reproduce the observed data. For all but the most trivial of models finding the global optima is very challenging. The constants for the SCE algorithm can significantly affect the results and the parameter range in which the algorithm searches may not include the global optima. For this section, please apply the SCE algorithm (code is supplied) and assess whether you have achieved a reliable solution.

This can be done as follows.

1. As good practice, you should show that the results of any optimisation are independent of the settings for the optimisation algorithm. We have given you reliable values for ngs, pcento and maxn; however, you need to show that your solution is independent of the number of complexes

i.e. SCE setting kstop. You should demonstrate that SCE is reaching a similar optima when different values of kstop are used. To do this, run SCE with a variety of values of kstop (say 10) and plot the resulting optimal objective function value. The algorithm should reach a consistent result as kstop increases.

2. With optimisation, you should always evaluate the repeatability of you results for given settings. To do this, you should run SCE several times for you final kstop and show that you get practically consistent (not necessarily identical, given there is some randomness in the algorithm) results when you rerun SCE using identical settings.

For this section, your report should:

? outline your calibration procedure;

? provide evidence to support your estimate of the global optima (i.e. why do you think you have found the global optima?);

? detail the adequacy and limitations of the calibration scheme;

? provide an evaluation of the model and in particular estimate the normalized sum of squared error = SSE / sum[(Observed – mean(Observed))]2 – this is used in Regional Sensitivity and GLUE codes; and

? critique your overall approach.

Finally, to assist in running the SCE algorithm, example MATLAB commands for the model are given in the header of the relevant SCE_calibration code and in the overview of MatLab functions for this assignment.

2 Regional sensitivity analysis (RSA)

The aim of Regional Sensitivity Analysis is to understand the relationships between the model

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predictions and the parameters using a form of global sensitivity analysis. This is based on a Monte Carlo analysis of the model. We have supplied Regional Sensitivity Analysis code that you can use. This code outputs the parameters and performance assessments for each Monte Carlo run. To speed up run times, you can generate a set of runs and save the results of those runs for later analysis. There is always a trade-off between run time and the number of simulations conducted (and hence the precision of your later analyses). We are not expecting you to use more than one hour of computation time to produce your final set of Monte Carlo model runs.

See the code overview for some hints on reusing model runs to save time.

The outputs that need to be saved for subsequent analysis are:

? The parameter values for each run;

? The simulated output (flow); and

? The model performance metrics you need to analyse.

For this section, your report should provide an interpretation of results of the RSA (both the cumulative distribution function plots and the plotmatrix plots) in terms of:

? how sensitive the model results are to each parameter;

? whether there are significant parameter interactions;

? which parameters are most likely to be identifiable through optimisation;

? what limitations there might be for this analysis; and

? what implications there are for choosing GLUE threshold levels.

3 Parameter uncertainty analysis

Having now undertaken both the global optimisation and the sensitivity analysis, it is now time to focus in on how uncertain each of the parameters you have identified is and what implications this has for the model predictions. This involves further using your set of Monte Carlo runs to undertake a parameter uncertainty analysis and rerunning the model for a subset of the Monte Carlo runs to explore how the parameter uncertainty feeds through to prediction uncertainty. Once you have finished the above calibration and RSA, you need to make some assessment of the parameter uncertainty. To estimate the parameter uncertainty, please use the Generalised Likelihood Uncertainty Estimation (GLUE) methodology.

An important aspect of GLUE is the selection of the threshold performance to consider a run as behavioural. In the light of your optimisation and the exploration of the model in the RSA, you need to choose a threshold performance level. This requires some judgement about what is and what is not an acceptable model performance and this decision should be discussed when you write up your report. Those model runs that meet the threshold (perform well enough) are then identified and their parameters obtained. You can gain some insight into an appropriate level for the threshold by comparing the uncertainty limits with the observed data; however, the GLUE analysis does not necessarily represent all uncertainty. Lastly, an estimate of the uncertainty is achieved by

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summarising the parameters that result in an acceptable simulation.

To help you apply GLUE, we have written MATLAB code for the GLUE framework. See the MatLab code overview document for more details. You should analyse the estimated parameter uncertainties and critique your overall approach. Below are some points to consider when running and/or critiquing your results.

1. We have supplied upper and lower bounds for each parameter. You should assess whether you think these are satisfactory, too narrow or too wide and whether your results are independent of this decision. You should consider the results of your RSA as a preliminary basis for making this decision and then revisit it following your GLUE analysis.

2. The number of parameter samples (realisations) determines how well the response surface is characterised. Set this large enough that your results are independent of this setting but not so large that GLUE takes a prohibitively long time to run. There may be trade-offs in setting the number of samples and the reliability. This should be discussed in your report. (If you are using pre-saved runs, this will be quicker – see MatLab overview)

3. Implementing GLUE requires a choice of the maximum acceptable error for a model to be considered behavioural, which can be challenging. Please clearly discuss and critique your choice.

4. To summarise the parameter uncertainties, there are a number of options. One option is to create box-plots for each parameter that communicates the parameter distributions. Another option is to plot the cumulative likelihood against parameter values. As such plots do not communicate the parameter interactions, you may also want to consider a more advanced plotting function called 'plotmatrix'. Plotmatrix produces a histogram for each parameter as well as scatter plots of each parameter against the others to communicate parameter interactions (see the RSA code for an example).

Note the similarities in RSA and GLUE and take this into account when writing your report.

Once you have completed the above, discuss the findings, any parameter interactions, and the adequacy of your method. You may want to review Beven (2001) to better understand the GLUE methodology.

4 Hydroelectric power plant reliability assessment and climate change assessment

Now that the model has been calibrated, the model can be used to make predictions. By also using the parameter uncertainties, the prediction error can be quantified. This part of the assignment looks at the reliability of a hydroelectric power plant used to meet peak demands. The demandData variable supplied has the component of the overall electricity demand that the hydroelectric generation needs to meet. The hydroPower function calculates both the reliability in time (the proportion of days demand is fully met) and also the proportion of the peak demand that the scheme is able to meet. Both the impacts of model uncertainty and climate change lead to uncertainty in the hydroelectric system operation.

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There are two tasks here:

1. Using the model outputs evaluate the reliability of the hydro power generation based on the modelled outflow from the catchment. Also find the reliability of the design in meeting the energy demands. Some useful information is given below.

? Catchment area = 153 km2

? Head = 220m

? Storage capacity 40,000ML

? Initial storage in the dam = 20,000ML

2. Assess the impact of climate change on the reliability of the hydropower generation by calculating the reliability of the design in meeting the energy demands under a 20% reduction in rainfall.

In writing up your assessment of the hydroelectric power system reliability, you should evaluate how well you think these uncertainties have been captured and comment on potential improvements in the method that you can think of. Comment on other potential sources of uncertainty.

5 Discussion and conclusions

Lastly, in your report you need to critique all of your modelling for this assignment and summarise the findings from each part of the model analysis including the reliability of your predictions.

5.1.1 References

Beven, K. (2001), Rainfall-runoff modelling: the primer, J. Wiley, , xi, 360