What can Statistics do for me?

Marian ScottDept of Statistics, University of Glasgow

Statistics course, September 2007

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

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?

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

so2 monitored in GB02

observations

so2

0 50 100 150 200 250

02

46

81

0

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

months

so2

1980 1985 1990 1995

02

46

81

0

Comments on the issue

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: particles on a beach

Discovery of radioactive particles on the foreshore of a nuclear facility since 1983

Is the rate of finds falling off? Are the particle characteristics changing with

time?

Why?, there have been a number of campaigns to recover the particles

Log activity and trend

Date

logact

ivity

20.0

17.5

15.0

12.5

10.0

7.5

5.0

Accuracy MeasuresMAPE 11.8851MAD 1.4229MSD 3.8787

VariableActualFits

Trend Analysis Plot for logactivityLinear Trend Model

Yt = 14.9899 - 0.00712072*t

Trend in number of finds

year

number of finds

2002200019981996199419921990198819861984

25

20

15

10

5

0

Accuracy MeasuresMAPE 108.951MAD 4.025MSD 28.222

VariableActualFits

Trend Analysis Plot for number of findsLinear Trend Model

Yt = 14.7476 - 0.401299*t

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

Spatial variation is clear There is variation amongst the measurement

techniques There are many ways of exploring the

important features There is uncertainty about the spatial extent

NERC priorities

climate change and more generally environmental change;

earth’s life support system; sustainable economies and environment and human health

where some of the fundamental research questions associated with each of these priorities require quantitative skills involving:   

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 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

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

Warming in the Arctic is double that for the globe from 19th to 21st century and from late 1960s to present.

Warmth 1925 to 1950 in Arctic was not as widespread as recent global warmth.

Note different scales

Arctic vs Global annual temperature anomalies (°C)

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.

What is the state and trend in biodiversity (EEA CSI 009)

Populations of common and widespread farmland bird species in 2003 are only 71% of their 1980 levels.

Key message: Butterfly and bird species across Europe show population declines of between -2% and -37% since the early 1970s.

What can we do? Biodiversity convention

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

Visualisation

Time series plots

Bar charts

Smoothers

Linear regression

Space and time

Pairs of images

Statistical modelling

Smoothers

Linear regression

a ) estimate of m 1 ( Year ) for log Chla

Year, in months

m1(

Year

)

1990 1994 1998 2002

-2-1

01

23

b ) estimate of m 2 ( Month ) for log Chla

Months

m2(

Mon

th)

2 4 6 8 10 12

-2-1

01

23

c ) estimate of m 3 ( log SRP ) for log Chla

log(SRP, mug/l)

m3(

log

SRP)

1 2 3 4

-2-1

01

23

d ) estimate of m 4 ( log Daphnia ) for log Chla

log(Daphnia, individuals/l)

m4(

log

Daph

nia

)

-4 -2 0 2 4

-2-1

01

23

e ) estimate of m 5 ( Water Temp ) for log Chla

Water Temp, oC

m5(

Wat

er Te

mp)

5 10 15 20

-2-1

01

23

f ) estimate of m 6 ( log NO3N ) for log Chla

log(NO3N, mg/l)

m6(

log

NO3N

)

-4 -3 -2 -1 0 1

-2-1

01

23

Additive models

Evidence-base for policy and management

“The integration of experience, judgement and expertise with the best available external evidence from systematic research”

(Davis, 1991)“….opinions and judgements of experts that constitute high quality, valid

and reliable evidence”

Modernising government requires to“produce policies that really deal with problems: that are forward looking

and shaped by the evidence……, that tackle causes not symptoms”Cabinet Office,

1999 Much policy making happens in response to very short-term

pressures – “Timely findings of practical relevance”

Effects of policy

“How much or how little we know about the links between environmental policy measures and their actual impact in the environment”

“much of the information gathered is of limited use in assessing the impact of environmental measures”

(Nigel Haigh, foreword of Environmental Issues, Report 25/EC)Agencies are ‘data rich and information poor.

“Good policy needs a foundation in good science.”(Margot Wallstrom, European Environment state and outlook report, 29 Nov 2005)

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”