environmental change and statistical trends – some examples marian scott dept of statistics,...
TRANSCRIPT
Environmental change and statistical trends – some examples
Marian ScottDept of Statistics, University of Glasgow
NERC September 2011
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
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: 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
403632282420161284
25
20
15
10
5
time
level
Time Series Plot
some simple examples
403632282420161284
25
20
15
10
5
time
level
Time Series Plot
403632282420161284
25
20
15
10
5
Index
10+
15
Time Series Plot of 10+15
403632282420161284
25
20
15
10
5
Index
10+
15(3
)
Time Series Plot of 10+15(3)
403632282420161284
25
20
15
10
5
Index
10+
15(4
)
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
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
Main question: – what is the long term trend and is it the same over Europe?
02
04
06
0
1984 1988 1992 1996 2000
daily SO2, monitored at Stoke ferry
days
SO
2;
ug
S/m
3
-20
24
1984 1988 1992 1996 2000
weekly means of the natural log of daily SO2, monitored at Stoke ferry
weeks in year
log
(S
O2
; u
g S
/m3
)
-20
24
1984 1988 1992 1996 2000
natural log of daily SO2, monitored at Stoke ferry
days
log
( S
O2
;
ug
S/m
3 )
Additive models 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) +
time and space interaction
The movie highlights the spatial adjustments that should be added to the main effect for space at particular time points.
Easting
Nor
thin
g
Spatial Trend
Interaction between space and time
TON for Coquet, Wansbeck, Blyth LHA in the NE (1994 - 2009)
Claire Miller, Ana Maria Magdalena, Adrian Bowman
Measurement and assessment of change-three questions to consider
Is routine monitoring data useful/adequate/sufficient for environmental change detection?
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?
how long does a time series need to be?
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
R script in CETcasestudy explore the trend (linear or otherwise) is the trend the same in the different months does the starting point matter in our
conclusions?
Case study 2: haddocks
R script in haddock explore the trend (linear or otherwise) Think about projections