Environmental change and statistical trends – some examples

1. Environmental change and statistical trends – some examples Marian Scott Dept of Statistics, University of Glasgow NERC January 2014

2. questions about trends and change • one of the most common questions • common in official and policy documents- often based on simple indicators • draws together much of preceeding technical sessions- time series, regression, even spatial… • some challenging issues to consider

3. questions about trends and change • How should we describe the trend? • Is there are seasonal component? • Are the data autocorrelated? • Are there any discontinuities or changepoints? • some challenging issues to consider

4. 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.

5. 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.

6. Measurement and assessment of change • What it the status quo in environmental science? • In time • A simple trend line • A p-value or a 95% confidence interval for the slope • A smooth curve • The relative change in an index between two time points (%) Is this sufficient?

7. Measurement and assessment of change- common tools • In time (SNIFFER, 2006) • A linear regression equation was calculated for each dataset and then the trend was calculated from the gradient parameter (i.e. the rate of change) multiplied by the length of the data period to provide a clear change value since the start of the period. • “the significance of trends was tested using the non-parametric Mann-Kendall tau test (Sneyers, 1990). Linear trends with the Mann-Kendall significance test are widely used in the analysis of climate trends”

8. Trends

9. Joint Nature Conservation Council definition of trend • a trend is a measurement of change derived from a comparison of the results of two or more statistics. • A trend relates to a range of dates spanning the statistics from which it is derived, e.g. 1996 - 2000. A trend will generally be expressed as a percentage change (+ for an increase, - for a decrease) or as an index.

10. Statistical definition of trend • What is a statistical trend? • A long-term change in the mean level (Chatfield, 1996) • Long-term movement (Kendall and Ord, 1990) • The non-random function (t)= E (Y(t)) (Diggle, 1990) • Trend is a long-term behaviour of the process, trends in mean, variance and extremes may be of interest (Chandler, this course) • Environmental change often but not always means a statistical trend • Not restricted to linear (or even monotonic) trends

11. Statistical tools for exploring and quantifying trend • Exploratory tools • Time series plots, smoothed trends over time (are the series equally spaced, no missing data?) • More formal tools • Can you assume monotonicity?, is the trend linear? • Non-parametric estimation and testing (classic tests) • Semi-parametric and non-parametric additive models (for irregular spaced data) • what is monotonic? steadily increasing or decreasing

12. Things we might want to watch out for

13. Example 1: a linear trend two time series- what are the trends? are they monotonic?

14. Example 1: a non-monotonic trend two time series- what are the trends? are they monotonic?

15. Example 2: The river Nile data • Volume of the river for approx 100 year period. • is there evidence of a change? • if yes, when and in what way?

16. a non-parametric model for the Nile • a smooth function (LOESS) or non-parametric regression model • OK? • any suggestion that there may be a change-point? (which is what?)

17. the simple problem – change in mean value • here we imagine a series with two mean levels • 20 observations N(10,22 ) and 20 observations N(20, 22) • our ability to detect a change depends on the size of the change and the variability in the series

18. some simple examples

19. ‘exploring whether a changepoint exists • principle for this method concerns a comparison of a left and right smooth and difference between them • confidence bands indicated, look for whether the left and right smooths leave the blue band

20. An alternative model for the Nile • two smooth sections, broken at roughly 1900. • different mean levels in the two periods • so modelling the two periods separately

21. Unequally spaced data • what are the sources of the irregularity? • roughly regular (every month but a different day) • missing observations (over the Xmas vacation) • can’t use ACF (use variogram instead) • can I plug the hole (if missing data) • a qualified yes, if gap is not too large, the reason for the missing data is not related to the values • how? • interpolation (say fill in with annual mean) • build a simple seasonal model

22. Example: trends in atmospheric SO2 levels over space- EMEP network • Daily measurements made at more than 100 monitoring stations over a 20 year period over Europe: • Complex statistical model developed to describe the pattern, the model portions the variation to ‘trend’, seasonality, residual variation and to include changepoints • Main question: • what is the long term trend and is it the same over Europe?

24. Additive models for trend but including space ln(SO2) = fym(years, months) + fll(latitude, longitude) +  ln(SO2) = fy(years) + fm(months) + fll(latitude, longitude) +  with appropriate assumptions on 

25. ln(SO2) = fym(years, months) + fll(latitude, longitude) +  ln(SO2) = fy(years) + fm(months) + fll(latitude, longitude) + 

26. Measurement and assessment of change-three questions to consider • Is routine monitoring data useful/adequate/sufficient for environmental change detection? • how long does a time series need to be? • Are the classical (well accepted) simple procedures such as • the % change between two time points (the slope), • A p-value or a 95% confidence interval for the slope sufficient for the complexity of environmental behaviour? • What do ‘statistical trends’ offer to evaluation of environmental change, to management and to policy setting?

27. Statistical trends and environmental change • Sophisticated statistical models for trends can give • added value and better descriptions of complex change behaviour and • begin to tease out climate change driven effects in environmental quality

28. Case study 1: Central England temperature • Central England temperature record, annual and monthly temperature data over several hundred years • R script in CETcasestudy • explore the trend (linear or otherwise) • is the trend the same in the different months?

29. Case study 2: haddocks • Fish stock evaluated on an annual basis, what is the trend, and can we project into the future • R script in haddock • explore the trend (linear or otherwise) • Think about projections