Environmental statistics
Lecture 1
Marian Scott
room 220
session 14/15
Outline of course
There
are a variety of assessments depending
on which programme you are studying (M level
and MSc have an additional assignment)
Two lab reports, and a case study f
Wednesday, 7th May 2014
09.30 am 11.00 am
EXAMINATION FOR THE DEGREES OF M.A., M.SCI AND B.SC. (SCIENCE)
ENVIRONMENTAL STATISTICS
Hand calculators with simple basic functions (log, exp, square root, etc.) may be used in
examinations. No calculator which c
Example sheet 1, solutions for Qns 4
4 general approach would be to used a a formula for the approximate variance of a function
of random van'ables
Y= f(X1, ...,Xn), then the approximate variance of Y is given by where pi and oi are expected
value and
Environmental statisticslecture 3/4
Modelling variability and handling
uncertainty
Marian Scott
room 220
session 14/15
what we will cover
Distributions:
Normal, Poisson, lognormal
extreme value distributions Gamma, Weibull,
Pareto and GEV
dealing wi
Spatial point processes
A Spatial point process is a set of locations, irregularly distributed
within a designated region and presumed to have been generated
by some form of stochastic (random) mechanism  Diggle (2003).
A realisation from a spatial point
School of Mathematics and Statistics
Environmental Statistics
Session 14/15
Example sheet 1: Censoring, uncertainty, limits of detection
A: censoring and uncertainty calculations
1. Limits of detection review the Eastoe paper (as discussed in the lecture
STATISTICS 4H/M
Environmental Statistics Practical 1
Session 14/15
Aims and intended learning outcomes
To explore graphically some environmental data sets
To consider graphical representations of some environmental time series
To explore trends using line
School of Mathematics and Statistics
Session 14/15
Example sheet 2: Environmental Statistics
Several of these examples are similar in nature to exam questions, in that you are
asked to comment on statements being made or on analysis already completed.
1.
STATISTICS 4H/M
Environmental Statistics Practical 2
Session 14/15
Spatial analysis and dealing with extremes
Aims and intended learning outcomes
To explore a quantile regression example and to interpret the output
To examine and interpret some geostatist
Solutions to Env Stats 2014 (level H and M)
1 a) Trend has been defined in a variety of ways
A longterm change in the mean level
Longterm movement
The nonrandom function (t)= E (Y(t)
Trend is a longterm behaviour of the process, trends in mean, va
?
?
EXAMINATION FOR THE DEGREE OF M.SC. (TAUGHT)
ENVIRONMENTAL STATISTICS Aquatic and Freshwater Sciences
Hand calculators with simple basic functions (log, exp, square root, etc.) may be used in
examinations. No calculator which can store or display text
Some real life changepoint
issues
Whitelees wind farm with Susan
Waldron, Helen Murray and
Fraser Tough
The site
Outline
key question:what is the effect of the
windfarm development?
A) impact assessment BACI
B) changepoint analysis
C) time series mod
Additional formula sheet for Environmental Statistics, 20142015
Probability distributions for Extremes
Generalised Extreme Value (GEV) distribution, has three parameters, location, scale
and shape (usually written as m, s(>0) and x)
G(z) =expcfw_[1+ x(z
Spatial modelling
Lecture
what
11/12
will we cover?
types of spatial data
spatial correlations
statistical models for spatial data
mapping
some examples
Case
1: point processes (like location of trees
in a forest)
Case 2: continuous case mapping
~W (1) in ecological sciences in time

A simple trend line
A pvalue or a 95% confidence interval for the slope
A smooth curve
The relative change in an index between two time points(%)
A linear regression equation was calculated for each dataset and the
some more information about
indicators
Measuring biodiversity
Composite indices
The 2010 Biodiversity target
To
significantly reduce the rate of biodiversity
loss by 2010
European Member States went further:
To
halt the decline of biodiversity in the EU
Sampling and monitoring (contd)
B:
designing monitoring experiments
Outline
goals:
to detect unexpected changes and
trends
standard
statistical sampling schemes are
adequate, but there are special cases:
random sampling, good spatial cover, and
gradua
School of Mathematics and Statistics
Session 14/15
Example sheet 3: Environmental Statistics
1. If X1,., is a sequence of independent standard exponential Exp(1) variables,
a. show that F(x)= 1ex for x> 0.
b. Show that for an=1 and bn=log n, the limit d
Example sheet 1, solutions for Qns 4
4 general approach would be to used a a formula for the approximate variance of a function
of random variables
Y= f(X1, ,Xn), then the approximate variance of Y is given by where i and i are expected
value and standard
Section 3:
Trend Analysis
Analysis of Climate and Weather Data  Trend Analysis  HS 2014  christoph.frei [at] meteoswiss.ch
1
Outline
General Concept
Parametric and NonParametric Trend Tests
Accounting for Serial Correlation
Trend Analysis for Count Da
Uncertainties
Example
IPCC produced guidelines on two approaches to the
uncertainty calculations for greenhouse gas emissions.
Total greenhouse gas emissions, C, for a given year
are calculated as
C = ei Ai
where ei and Ai are the emissions from and acti
DetectionandEstimation
Detection
MannKendall statistic
Seasonal Kendall trend test
Heterogeneity
Serial Correlation
1
FromEEA,2013,ozonetrends
2
The MannKendall statistic for season j
sgn(x) =1 if x < 0
0 if x = 0
1 if x > 0
Hypothesis: random sample of
Environmental statistics
Summary points
what have we covered and what
should you know?
Outline
Exam is on: 21st May
Time: 14.0015.30
Venue: Hunter Hall East
(double check this with the published exam timetables)
You will have statistical tables, the En
Time series modelling and
statistical trends
lectures 7 and 8
Environmental Statistics
session 14/15
1
what is a time
series?
a time series is a sequence of measurements
made over time.
notationally, this would commonly be written as
y1, y2, yi, .yT
th
Simple metrics, complex
environmental systems
Environmental indicators
Outline
why do we need environmental indicators?
various examples of environmental indicators
potential advantages and disadvantages
Creating composite indicators or indices
Statistica
Environmental Statistics
Lab 1 draft solution 2014/2015
Mauna Loa
Tasks
For the Mauna Loa data, read up some of the history of the site, and use this to construct
your introduction to this key data set.
Plot the time series in variety of ways, fit a simpl
Probability distributions
Marian Scott
An expert judgement assessment
of future sea level rise from the ice
sheets
J. L. Bamber1* and W. P. Aspinall2
Nature Climate Change 2013
Lab 2 solution 2015
Ozone levels at Bush
A report should include an introduction to the problem, so here that would be a brief
discussion about the importance of ozone as an air pollutant, a brief description of the
statistical methodology to be used, you
Environmental statisticslecture 5/6
A:
Sampling and monitoring general
B:
designing monitoring networks
Outline
Statistical
sampling strategies and
applicability to environmental sciences,
Principles and practice
An example
some analysis approache