What can Statistics do for me?

Marian ScottDept of Statistics, University of Glasgow

Statistics course, August 2009

Outline of presentation

Why would or indeed should an environmental scientist need to know any statistics?

Illustration: environmental change- one of the most enduring features with– Links to research, policy, policy effectiveness

evaluation,policy and management

Why quantify?

Quantification is an essential part of most scientific activities

For the environment, quantification must account

– for inherent variability of the process or

– for lack of precise knowledge of it

and is needed for resolving many of the environmental issues of today

Decision making- Which areas should be restricted?

Prediction-What is the trend in temperature? Predict its level in 2050?

Decision making-is it safe to eat fish?

Regulatory- Have emission control agreements reduced air pollutants?

Understanding -when did things happen in the past

Some examples of current environmental issues…….

Climate change Biodiversity Arctic ice cover Water quality Extreme weather

Direct Observations of Recent Climate Change

Gobal mean temperature

Global averagesea level

Northern hemisphereSnow cover

Trends in seasons over Europe (Global Change Biology, 2006)

21 countries, 125,000 studies, 542 plant and 19 animal species, 1971-2000

Spring is on average 6 to 8 days earlier than it was 30 years ago

Analysis of 254 national time series , pattern of observed change in spring matches measured national warming (correlation coefficient –0.69, P<0.001)

Observed temperature trend in Europe (EEA signals 2004).

Global average temp increased by 0.70.2°C over the past 100 years

Change in different periods of the year may have different effects,

– start of the growing season determined by spring and autumn temps,

– changes in winter important for species survival.

Spatial patterns of change

Spatial patterns of change may be important

Changes in the start and end of the growing season between two years (1961, 2004)

– heterogeneous

Example: are atmospheric SO2 concentrations declining?

Measurements made at a monitoring station over a 20 year period

Complex statistical model developed to describe the pattern, the model portions the variation to ‘trend’, seasonality, residual variation

Quantification is model and observation basedQuestions about the model Is it valid? Are the

assumptions reasonable? Does the model make sense

based on best scientific knowledge?

Is the model credible? Do the model predictions match the observed data?

How uncertain are the results?

Questions we ask about data Do they result from

observational or designed; laboratory or field experiments? What scale are they collected over (time and space)?

Are they representative? Are they qualitative or quantitative?

How are they connected to processes, how well understood are these connections?

How uncertain are they?

so2 monitored in GB02

observations

so2

0 50 100 150 200 250

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Plot of so2 against time, monitored in GB02Lines = Model 3

months

so2

1980 1985 1990 1995

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Comments on the issue

Statistical theme- time series modelling, trend detection

Lots of variation Variation may make the pattern more difficult to

see (signal to noise ratio) There may be small numbers of unusual

observations There may be distinct changes (discontinuities)

Example 2: water quality

catchment modellingWFD requires basin management plans: measurement series covers 20 years,

including a variety of biological, chemical and hydrological indicators but irregular in time. Stations appear and disappear

Joint work with David O’Donnell, Mark Hallard (SEPA), Adrian Bowman

Spatial patterns of change

Spatial patterns of change may be important

the circles represent the stations on the network, clearly not spatially representative

Spatial patterns of change

Spatial patterns of change may be important

interpolation over the entire network from the stations is possible, but needs a spatial model

Example: how is Cs-137 distributed over a large area of SW Scotland?

Aerial survey of the area (detectors mounted in helicopters)

How to design the flight pattern (straight lines separated by 250m)?

How to match and then calibrate the results to ground based measurements?

137Cs deposition maps in SW Scotland prepared by different European teams (ECCOMAGS, 2002)

Lochs in area Y

comments on examples

Statistical themes- where to sample, and whether representative, spatial modelling

Aerial survey-how to design the flight pattern (straight lines separated by 250m)?

How to match and then calibrate the results to ground based measurements?

Comments

Spatial variation is clear There is variation amongst the measurement

techniques There are many ways of exploring the

important spatial features There is uncertainty about the spatial extent

Example-Bathing water quality

All bathing water sites are classified as either ‘Excellent’, ‘Good’, ‘Sufficient’ or ‘Poor’ in terms of the quantities of 2 different microbiological indicator bacteria

Faecal Streptococci (FS)Faecal Coliforms (FC)

‘Sufficient’ is the minimum standard that bathing water sites are required to meet

Classification for each site is based on the 90th & 95th percentiles of samples over the most recent 4 bathing seasons

joint work with Ruth Haggarty, Claire Ferguson

Boxplots show distribution of FS with respect to guideline limits Green line represents EC Directive threshold for ‘Excellent’ (95th percentile evaluation) Red line represents EC Directive threshold for ‘Good’ (90th percentile evaluation) Blue line represents EC Directive threshold for ‘Sufficient’ (90th percentile evaluation)

2004 2005 2006 2007

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Boxplots of FS: Portobello Central

SEPA location code 4593Year

FS

2004 2005 2006 2007

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Boxplots of FS: Sandyhills

SEPA location code 114567Year

FS

2004 2005 2006 2007

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Boxplots of FS: Saltcoats/Ardrossan

SEPA location code 124673Year

FS

2004 2005 2006 2007

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Boxplots of FS: Irvine

SEPA location code 124688Year

FS

2004 2005 2006 2007

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Boxplots of FS: Troon

SEPA location code 124706Year

FS

2004 2005 2006 2007

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Boxplots of FS: Prestwick

SEPA location code 124714Year

FS

2004 2005 2006 2007

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Boxplots of FS: Ayr

SEPA location code 124725Year

FS

2004 2005 2006 2007

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Boxplots of FS: Brighouse Bay

SEPA location code 124793Year

FS

2004 2005 2006 2007

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Boxplots of FS: Ettrick Bay

SEPA location code 124817Year

FS

2004 2005 2006 2007

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Boxplots of FS: Aberdeen

SEPA location code 233616Year

FS

Bimodality

Evidence of bimodality at some sites

This can result in the four year 95th percentile appearing greater than the maximum value within a single year

7206004803602401200

2004

2005

2006

2007

FS (per 100ml)

Year

Dotplot of FS for SandyhillsSEPA Location Code: 114567

90th Percentile95th Percentile

Assessment of Distribution

It is believed that samples have come from a log10 normal population at each site. Directive gives directions for calculating percentiles on the assumption that the data follows a log10 normal distribution

Assumption of log-normality is needed for accurate calculation of percentiles and consequently accurate compliance classification of sites

Histogram of FS

SEPA location code: 4556FS/100ml

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nsi

ty

0 20 40 60 80 100

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Normal Q-Q Plot

Theoretical Quantiles

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Histogram of log10(FS)

SEPA location code: 4556log10(FS)/100ml

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nsi

ty

0.0 0.5 1.0 1.5 2.0

0.0

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-2 -1 0 1 2

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Normal Q-Q Plot

Theoretical Quantiles

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0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

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FS: Site 233613

Theoretical Percentile (log10 scale): 2.63x

Fn

(x)

2.63-0.5 0.0 0.5 1.0 1.5 2.0

0.0

0.2

0.4

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FS: Site 235334

Theoretical Percentile (log10 scale): 1.48x

Fn

(x)

1.48 1.52

Theoretical Percentile

Empirical Percentile

Log scale 1.48 1.52

Directive Scale 30.2 33.11

Theoretical Percentile

Empirical Percentile

Log scale 2.62 2.62

Directive Scale 416.9 416.9

comments on example

statistical themes- distributional assumptions to be tested, extreme value modelling 

considerable variation both within sites over years and across sites  

unusual observations appear

NERC priorities

the climate system biodiversity environment, pollution and human health sustainable use of natural resources earth system science;

Goals include responding to climate change and predicting impacts of environmental change . Some of the fundamental research questions associated with each of these priorities require quantitative skills involving:   

Statistics might be needed where?

designing and evaluation monitoring and sampling networks; sampling strategies

the analysis of observational records, (e.g. past climate indicators, water quality, pollutant trends); trends, spatio-temporal modelling, dealing with variation

the study and modelling of extreme events (e.g. sea levels, flood prediction) for prediction and management of future occurrences; extremes, risk modelling, uncertainty

evaluating the state of the environment;trends, uncertainty, prediction

Statistics might be needed where?

the use of complex computer models to simulate the whole earth system (e.g. climate change and the carbon cycle); uncertainty, model evaluation

the analysis of observational records, (e.g. past climate indicators, water quality, pollutant trends); trends, spatio-temporal modelling, dealing with variation

the study and modelling of extreme events (e.g. sea levels, flood prediction) for prediction and management of future occurrences; extremes

the evaluation and quantification of risk and uncertainty (e.g. volcanic or earthquake prediction);uncertainty, prediction

Statistics and the environment

Appropriate statistical models can give – added value to routine monitoring data, – better descriptions of complex change behaviour

and – begin to tease out climate change driven effects in

environmental quality – handle natural variation.

Greater, innovative statistical analysis needed for environmental science

Statistics and the environment

As environmental scientists, we need to try and ensure that:

data are gathered under good statistical principles and that they are not left in the filing cabinet.

We need to ensure thatGood environmental science is served by good statistical science.

Environmental science should be “Data and information rich”

Statistics training

we have chosen a number of key statistical topics to cover- there are many others

each topic will be covered in a general sense but will also have practical examples for you to work through with guidance

the main software tool will be R, which is freely available

there should be lots of opportunities to ask questions