EART60061 M&P1

 WEEK1: Introduction

Q1: Thinking about our learning

1. trained people can solve a particular problem, educated people can solve a wider range of problems.

2. Because environmental problems are rarely specific to a single subject, solutions are more likely to be improved by more education than training.

3. Whilst not the only selling point of an environmental scientist, the unique selling point(USP) is often an ability, achieved through education to recognise links between subject areas. 

Q3: What is research

1.Writing the theory of evolution, the theory of special relativity and plate tectonics were types of induction.  These ideas which may have been derived from synthesis of a large amount of previous work or "thought experiments"were related to the real world.  Probably a large amount of research based on deduction was carried out before the induction was accepted, this may then have resulted in a paradigm shift.

编写进化论、特殊相对论和板块构造理论是正确归纳的类型。这些观念可能源于对大量先前工作或“思维实验”的综合，与现实世界相关。在接受归纳之前，可能进行了大量基于正确演绎的研究，这可能随后导致了正确的范式转变。

2. Strictly a hypothesis should be falsifiable, effectively it must be possible to disprove.  However, falsifiability can be too strict because of the descriptive nature of some scientific research.  Falsifiability may also be misleading if it relies on observations/measurements that are highly impractical.  Nevertheless, falsifiability should be a researcher's initial goal in setting a hypothesis.

3. Using terminology explained at explorable.com write a few lines to describe the type of research that has the least risk of failure to gain a high mark, and explain why.

A piece of deductive research, testing whether some observations agree with an established theory.  Because time and resources are very limited for an MSc project it is neither likely that a novel theory can be induced nor that it could be sufficiently well tested to be accepted.

4. Research requires both inductive and deductive reasoning.  deductive  reasoning is often required to identify a research question or set up an aim. In mathematical research, deductive reasoning would then also be used to achieve the aim but in environmental science there will be more reliance on inductive.

5. Typically, reporting of research proceeds from explanation of a general problem; the requirement to solve this is then the aim of the work.  Having explained this a specific procedure to solve it must be developed, typically this requires that a set of subsidiary problems be solved; these are the objectives.  Defining these requires an argument that makes a clear connection of each to the aim.

A Research Proposal should justify the requirement for resources required to fund the activities detailed in the methods, the proposal must therefore make a clear argument that connects these activities to the aim of the work via the objectives.

WEEK2: Making measurement meaningful

Q1: Dialogue on the need to measure variability

Q: In which of the examples is it possible to measure the true value and why?

A: A true measurement of limpets on the shore could be made as limpets are discrete variables, however, quadrats would have to cover the entire survey area.

Given that measurement of the true value is only possible when variables are discrete and even then rarely possible, there is a requirement to somehow make measurement meaningful, this can be achieved by: Increasing the number of repetitions (multiple measurements).

Q:  How can this make measurement meaningful?

A: multiple measurement will increase the probability of better approximating the population (true) mean

Q: Why may this be insufficient to make measurement useful?

A: constraints of time and finance will always prevent the true mean being found

A: and no indication of the likelihood that the result is the true mean is given.

Q: How else may multiple measurements be more useful in making measurements meaningful?

A: The advantage of multiple measurements may not be predominantly to increase the probability of better approximating the population (true) mean

Consideration of the variability of the sample can give an indication of whether the sample mean is likely to be close to the true mean.  Such an indication is often the most appropriate way of making measurements useful, however, this presupposes that the scientist also knows the degree of difference from the true value that is acceptable for the study.

(It is important to note that the sample variability cannot be considered if the sample consists of a single measurement.)

Q2:Propagating errors

1. 

channel depth=1.5(0.2); width=0.7; flow=0.9(0.3); 0.945(0.1218) m3/ s

1day=24h=24*60min=24*3600s=86400s
81648m3

置信度不到95%

Q3: Deriving d-values

The % of the Normal distribution covered by a d-value of 2 is 97.72% this is not the value calculated in the "deriving d-value" exercise (to the same number of decimal places).  In order to get these numbers to match the resolution of the classes on the ssheet must be increased

Q4: 7 foot student?

What is the likelihood (in %) that there was a student taller than 7ft (1ft = 0.3m) at Manchester University in 2000?

Calculate how many standard deviations away from the mean is 7ft, and express the area under the curve (number of students in this height class) as a % of the whole area.

2.8874E-09 is the answer if the class interval of 5cm is used however the class interval 200-210cm is 10cm.  If 10cm is used the answer is 5.7748E-09, therefore the answer has a range from 2.8874E-09 and 5.7748E-09.

10cm is the correct class interval but either answer is acceptable - they both demonstrate that you understand how to use the distribution.

It would be best to add 2 classes - (200-205) and (205-210) - and calculate the probability of the 205-210 class as this is closer to the answering the question "what is the probability of a 7ft (210) student?)

Q5: Why are many measurements predictions?

Measurements of continuous variables inevitably have an associated error.  The error is quantified through multiple measurement and then the measurement is presented as a range within which it is predicted to lie.  Often the measurement is chosen to be the value predicted to occur at least 95% of the time.

连续变量的测量不可避免地伴随有误差。误差通过多次测量来进行量化，然后将测量结果呈现为一个范围，该范围内预测测量值有可能存在。通常，选择的测量值是被预测至少发生在95%的时间内的值。

Q6: Coastal contamination practice questions沿海污染

The following points are used in the introduction to a paper titled "Determination of the extent of coastal contamination around Anglesey UK"

place the points in the most appropriate order

Metal burden of Irish sea is known to be near EC limits

Description of site and geographical context (of NorthWest) – population urban centres, industrial and domestic discharges 

Parys Mountain was the largest Cu mine in the world at the beginning of the 19th Century

The site is now largely abandoned and subject to no controls

Metal flux from Parys Mountain exceeds that of the major rivers of the northwest 

High metal concentration in Afon Goch though low discharge

Q7: Do the analytical errors change your interpretation?

Does the information about the variability of the metal concentration measurements of the standards, blanks and reference materials, change your interpretation of the results of your Coastal Contamination paper?

No, because the variability (errors) in these analyses is much smaller than the variability in the natural material - the variability in the 10 samples of seaweed.

WEEK3: Prediction and Modelling + Predicting one variable from another

The failures that you have identified could be classified as:

Failure resulting from insufficient data

Failure resulting from poor understanding of the system e.g. dimisions

Why should attempts at prediciting behaviour of environmental systems be particularly prone容易 to these failures:

1 insufficient data: limited extent in the environment

2 poor understanding of the system

When would you consider a fitted curve to be a model? Is the example given a model:

can be consider as a model, because it represent an underlying relationship or pattern in a data.

Understanding of the system

a conceptual model must be formulated mathematically

1. One of the problems with conceptual models is that it may be difficult to formulate them mathematically.

True. This is especially the case when we're dealing with complicated conceptual models.

2. Mathematical models usually have only one type of solution.

False. These models have analytical solutions and numerical solutions.

3. Verification is a process that applies to any type of solution.

False. Verification applies to a numerical solution only, as it's not necessary in analytical solutions.

4. Model calibration refers to changing its underlying assumptions.

False. The term refers to changing some of the parameter values, usually done when model outputs don't match the real world.

Q1: Metal flux measurement

The metal flux from the Afon Goch to the sea was negative, however, this finding must be considered in the light of evidence, recognised from the sampling programme, that the flux is variable.

The flux was different between spring and neap tides.

Furthermore, fluxes on both days were dominated by particulate metal which has the potential to become immobilised in the estuary, thereby causing flux to be dependent on not only current conditions but also previous flux.

The observation of a large negative flux is in itself evidence that flux must be variable.  It is most likely that the days on which flux was sampled coincided with the flux that occurs most frequently.  However, given that there is a large source of metal inland a negative flux cannot be a continual occurrence; the average flux must in the long-term be positive.  If the flux is most frequently negative but the long-term average must be positive then positive fluxes must occur infrequently but be very high.从Afon Goch到海洋的金属通量是负的，然而，这一发现必须在采样计划中获得的证据的光下考虑，该证据表明通量是可变的。

通量在春潮和小潮之间有所不同。

此外，两天的通量都以颗粒状金属为主，颗粒状金属有可能在河口中变得不动，从而导致通量不仅依赖于当前条件，还依赖于先前的通量。

观察到大量的负通量本身就是通量必须是可变的证据。很可能采样通量的那几天巧合地与最常发生通量的那几天重合。然而，考虑到内陆存在大量金属源，负通量不能是持续发生的现象；平均通量在长期内必须是正的。如果通量最常为负，但长期平均必须为正，那么正通量必须是不经常发生但非常高的情况。

使用excel进行线性回归：选中数据，生成散点图，增加趋势，更多可以增加公式。

R平方（R2）是线性回归模型的拟合度量。

Q2: Rating curve

The simplest model of the relationship of concentration to discharge was a line of negative slope on the assumption that increase in discharge causes dilution .  This failed because it predicted that the concentration could become zero.  Dilution is actually represented by a power law and therefore to test whether this occurs the linearity of the data should be assessed after a double log transformation.

Some scatter may remain because the EC v Q relationship is time dependent this is because solute availability may vary with time.  To test whether this is the case the data should be separated into time periods.

Some scatter may remain because the solute is not homogeneous 同质each component has different provenance出处 and has a different response to Q.

Q3: Rainforest regrowth

Growth in site A is approximated by a logistic curve whilst that in site B is not.  The latter may be because its recovery is much slower and is, therefore, probably a long way from reaching its carrying capacity so estimates of K were inappropriate.  However, regrowth at site B does not appear to be exponential at any time during the study so the assumptions rather than just the parameters of the model may be inappropriate.

Exponential growth is usually a response to an environment where there are  no limits to growth, as site B was initially clear there can be no competition so the limitations that prevent initial exponential growth must be related to the soil. 

That growth was approximately exponential in site A suggests there were initially no limits to growth, the subsequent decrease in growth rate may have arisen because of competition for light or nutrients.

The parameters K and r (carrying capacity and specific growth rate) for the logistic model were estimated from the observed data.  The model was then validated by comparison to the observed data.  Goodness of fit was assessed by plotting observed against predicted and calculating the correlation coefficient 相关系数.  The model was calibrated by adjusting the estimates of K and r within the bounds of the observed data, until the fit was optimised.

Despite being calibrated校准 the model could not be validated at site B.