1. What can Statistics do for me? Marian Scott Dept of Statistics, University of Glasgow Statistics course, March 2009

2. 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

3. 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

4. Some examples of current environmental issues……. Climate change Biodiversity Arctic ice cover Water quality Extreme weather

5. Direct Observations of Recent Climate Change Gobal mean temperature Global average sea level Northern hemisphere Snow cover

6. 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)

7. Observed temperature trend in Europe (EEA signals 2004). Global average temp increased by 0.7 0.2°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.

8. 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

9. Example: are atmospheric SO 2 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

10. Quantification is model and observation based Questions 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?

13. 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)

14. Example 2: water quality catchment modelling WFD 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 ODonnell, Mark Hallard (SEPA), Adrian Bowman

15. Spatial patterns of change Spatial patterns of change may be important the circles represent the stations on the network, clearly not spatially representative

16. 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

17. 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?

18. 137Cs deposition maps in SW Scotland prepared by different European teams (ECCOMAGS, 2002)

19. Lochs in area Y

20. 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?

21. 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

22. 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 90 th & 95 th percentiles of samples over the most recent 4 bathing seasons joint work with Ruth Haggarty, Claire Ferguson

23. 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)

24. 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

25. Assessment of Distribution It is believed that samples have come from a log 10 normal population at each site. Directive gives directions for calculating percentiles on the assumption that the data follows a log 10 normal distribution Assumption of log-normality is needed for accurate calculation of percentiles and consequently accurate compliance classification of sites

27. Theoretical Percentile Empirical Percentile Log scale1.481.52 Directive Scale30.233.11 Theoretical Percentile Empirical Percentile Log scale2.62 Directive Scale416.9

28. 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

29. 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:

30. 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

31. 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

32. 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

33. 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 that Good environmental science is served by good statistical science. Environmental science should be Data and information rich

34. 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