Presentation on theme: "Environmental change and statistical trends – some examples"— Presentation transcript:
1Environmental change and statistical trends – some examples Marian ScottDept of Statistics, University of GlasgowNERC January 2014
2questions about trends and change one of the most common questionscommon in official and policy documents- often based on simple indicatorsdraws together much of preceeding technical sessions- time series, regression, even spatial…some challenging issues to consider
3questions 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
4Observed temperature trend in Europe (EEA signals 2004). Global average temp increased by 0.70.2°C over the past 100 yearsChange 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.
5What 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.
6Measurement and assessment of change What it the status quo in environmental science?In timeA simple trend lineA p-value or a 95% confidence interval for the slopeA smooth curveThe relative change in an index between two time points (%)Is this sufficient?
7Measurement 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”
9Joint 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 A trend will generally be expressed as a percentage change (+ for an increase, - for a decrease) or as an index.
10Statistical 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 trendNot restricted to linear (or even monotonic) trends
11Statistical tools for exploring and quantifying trend Exploratory toolsTime series plots, smoothed trends over time (are the series equally spaced, no missing data?)More formal toolsCan 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
13Example 1: a linear trend two time series- what are the trends? are they monotonic?
14Example 1: a non-monotonic trend two time series- what are the trends? are they monotonic?
15Example 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?
16a non-parametric model for the Nile a smooth function (LOESS) or non-parametric regression modelOK?any suggestion that there may be a change-point? (which is what?)
17the simple problem – change in mean value here we imagine a series with two mean levels20 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
19‘exploring whether a changepoint exists principle for this method concerns a comparison of a left and right smooth and difference between themconfidence bands indicated, look for whether the left and right smooths leave the blue band
20An alternative model for the Nile two smooth sections, broken at roughly 1900.different mean levels in the two periodsso modelling the two periods separately
21Unequally 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 valueshow?interpolation (say fill in with annual mean)build a simple seasonal model
22Example: 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 changepointsMain question:what is the long term trend and is it the same over Europe?
26Measurement 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 asthe % change between two time points (the slope),A p-value or a 95% confidence interval for the slopesufficient for the complexity of environmental behaviour?What do ‘statistical trends’ offer to evaluation of environmental change, to management and to policy setting?
27Statistical trends and environmental change Sophisticated statistical models for trends can giveadded value and better descriptions of complex change behaviour andbegin to tease out climate change driven effects in environmental quality
28Case study 1: Central England temperature Central England temperature record, annual and monthly temperature data over several hundred yearsR script in CETcasestudyexplore the trend (linear or otherwise)is the trend the same in the different months?
29Case study 2: haddocksFish stock evaluated on an annual basis, what is the trend, and can we project into the futureR script in haddockexplore the trend (linear or otherwise)Think about projections