Intensive course 050607 -- 050610
A Grimvall
Day 2: Trend analysis
Exercise 1: Meteorological normalisation of wet nitrogen
deposition in Sweden and Norway
A. Examine the raw data sets
The Excel file ‘Exercise1_dep_data.xls’ contains daily observations of precipitation
amount and concentrations of oxidized (nitrate) and reduced (ammonium) nitrogen in the
sampled precipitation. To be more precise the file contains data from two EMEP stations:
Rörvik in Sweden and Birkenes in Norway.
Examine the data collected at Rörvik by plotting observed deposition values vs
precipitation amount. Is there any difference in the patterns observed for ammonium and
nitrate, respectively?
Open MINITAB and copy the Rörvik data to this statistical software package. Click on
Stat>Basic statistics>Display descriptive statistics and enter data so that you obtain
graphs of simultaneous boxplots of ammonium concentration vs wind sector? Is there any
obvious concentration difference between the eight wind sectors (N, NO, O, SO, S, SV,
V, NV)? Do the concentration values to which no wind sector was assigned (code 9 in the
wind sector column) differ dramatically from the other concentration values?
Examine the Birkenes data briefly by plotting observed deposition values vs precipitation
amount.
B. Make a simple normalisation of the wet nitrate deposition at Rörvik
Copy the annual data regarding wet nitrate deposition at Rörvik from the Excel sheet to
MINITAB. Click on Stat>Regression>Regression and Storage>Residuals and regress
the nitrate deposition on the precipitation amount. Copy the residuals back to the Excel
sheet and create a new column where the mean the observed deposition values has been
added to the residuals. This column will then contain the precipitation-normalised wet
nitrogen deposition values.
Make a time-series plot where the ‘Observed* and ‘Normalised’ deposition values are
shown in the same diagram? Did the normalisation reduce the interannual variation? Did
the normalisation reveal any obvious trends in the deposition?
Intensive course 050607 -- 050610
A Grimvall
C. Meteorological normalisation of wet deposition data using
semiparametric regression models
In this task we shall refine the simple normalisation undertaken in task B. This will be
accomplished by using the VisualBasic macro Wetdepnorm that is run in the steps listed
below. The user’s manual contains a more detailed description.
Running the WETDEPNORM programme
Copy data to worksheets
Run macro 'Auditdailydata'
Enter and check
input data
Select analysis
on 'Model selection' worksheet
Run macro
'Matchprecipandconc'
Compute deposition
by sector or season
Run macro
'Compute_deposition'
Indicate response and explanatory
variables for the normalisation model
Run macro
'Definenormalisationmodels'
Run macro
'Wet_dep_normalise'
Define models
and compute
normalised values
Intensive course 050607 -- 050610
A Grimvall
Enter data
Copy the daily Rörvik data from the Excel document ‘Exercise1_dep_data.xls’ to
‘Wetdepnorm_1_0.xls’ according to the instructions given in the user’s manual for
Wetdepnorm.
Check input data
Activate the worksheet ‘Precip and sector by date’. Then run the macro ‘auditdailydata’
by clicking on Tools>Macro>Macros>auditdailydata. Repeat this procedure for the
worksheet ‘Concentration by date’. Consult the user’s manual if you receive any error
messages.
Compute the nitrate deposition by sector
Select analysis by sector on the sheet ‘Model selection’.
Match precipitation and concentration data running the macro 'Matchprecipandconc'.
Compute annual deposition values and annual values by sector (expressed in mg/m2/day)
by running the macro 'Compute_deposition'.
Define normalisation models
Activate the worksheet ‘Seasonal or sector totals’ and define normalisation models by: (i)
writing x or y two lines above each of the explanatory variables and response variables
you would like to include in your model(s), and (ii) running the macro
‘Definenormalisationmodels’.
Edit the list of models printed on the worksheet so that you can run models in which the
annual wet nitrate deposition by sector is regressed on precipitation amount and the
number of raindays per sector and year. Because each model takes approximately one
minute to run on an ordinary PC, you are recommended to start analysing one form of
nitrogen (nitrate, for example) at one site (Rörvik) and select at most two explanatory
variables.
Carry out the normalisation by running the macro ‘Wet_dep_normalise’, and inspect the
output on the sheet ‘Normalised annual totals’. (Note that the annual deposition values
are expressed in mg/m2/yr, if the concentration values are expressed in mg/l). Did the
semi-parametric normalisation (SP-regression) improve the normalisation in task B?
If there is time enough, the analysis above can be repeated for another site (Birkenes) or
another form of nitrogen (ammonium, for example). What conclusions can be drawn
regarding temporal trends in observed and normalised wet nitrogen deposition data at
Rörvik and Birkenes?
Intensive course 050607 -- 050610
A Grimvall
Exercise 2: Response surface modelling and trend analysis of
total nitrogen concentrations in the Stockholm archipelago
A. Examine the raw data sets
The Excel file ‘Exercise2_water_data.xls’ contains observations of total nitrogen
concentration (g/L), salinity (psu), water temperature (oC), and oxygen concentration
(mg/l) in water samples taken at different stations and different depths in the Stockholm
archipelago. To be more precise the file contains all February values from 1989 to 2004.
Furthermore, an indicator variable is added to distinguish between the inner and outer
parts (coded as 1 and 0, respectively) of the archipelago.
Examine the given water quality data by making simple plots of total nitrogen
concentrations vs sampling year and salinity for the subsets of data corresponding to the
inner and outer archipelago. Which temporal trends in the data are obvious?
B. Estimating a monotonic regression model of total nitrogen
concentrations in relation to sampling year and salinity
The Matlab program ‘GPAVMONNOR’ can be used to fit a monotonic regression
model to observations of a response variable in relation to sampling year and one or more
additional explanatory variables. This model can then be employed to normalise the
observed values of the response variable. GPAV stands for the ‘Generalized Pool
Adjacent Violators’ algorithm, which is an algorithm recently developed at Linköping
University.
Try to use the quick guide to monotonic regression to fit such a model to total nitrogen
concentrations in relation to sampling year, salinity and an indicator variable representing
sampling sites in the inner archipelago. The names of the input files are already given in
the Matlab code. The execution of the code takes about 2 minutes. You can receive the
fitted values by typing ‘Yhat’ in the Matlab command window.
C. Illustrate the estimated temporal trend
Worksheet ‘AllFeb data (2)’ in the Excel file ‘Exercise2_water_data.xls’ contains
observed as well as fitted response values. Check if the values you received in B are the
same as the ones given in the Excel file.
Illustrate the estimated temporal trend by plotting fitted total-N concentrations against
salinity for selected years. Is there a clear temporal trend at all salinity levels? Is the trend
present in both the inner and outer archipelago?
Intensive course 050607 -- 050610
A Grimvall
D. Validation of the monotonic regression model
Examine what fraction of the total variation in the concentrations of total nitrogen that
can be explained by sampling year and salinity. Is the model equally good in the outer
archipelago as in the inner?
Examine whether the fitted regression model can be improved by incorporating
additional explanatory variables.