Environmental change and statistical trends – some examples

Marian ScottDept of Statistics, University of Glasgow

NERC August 2012

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

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.

Climate change in Scotland (SNIFFER report, 2006)

Annual average 24-hour maximum temperature over 90 year period, in 3 regions of Scotland

– Very varied, non monotonic

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.

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?

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”

Trends

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.

 

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

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

Things we might want to watch out for

two time series- what are the trends? are they monotonic?

Example 1: an index of bird species population

two time series- what are the trends? are they monotonic?

Example 1: a linear trend

two time series- what are the trends? are they monotonic?

Example 1: a non-monotonic trend

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?

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?)

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

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some simple examples

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Time Series Plot of 10+15(3)

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Time Series Plot of 10+15(4)

‘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

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

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

Alternative statistical tools(for long, irregular time series, which may be non-

monotonic) already seen many of these

Parametric and semi-parametric models, non-parametric additive models Extensions to trends in space and time not especially useful for forecasting, but very

flexible to explain

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?

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daily SO2, monitored at Stoke ferry

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weekly means of the natural log of daily SO2, monitored at Stoke ferry

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natural log of daily SO2, monitored at Stoke ferry

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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

ln(SO2) = fy(years) + fm(months) + fll(latitude, longitude) +

ln(SO2) = fym(years, months) + fll(latitude, longitude) +

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?

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

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?

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