HOMOGENITY AND
HOMOGENIZATION METHODS.
A review.
Enric Aguilar
Climate Change Research Group
Geography Department
Universitat Rovira i Virgili de Tarragona (Spain)
enric.aguilar@urv.cat
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
OUTLINE
•
A few questions to start
–
–
–
–
–
•
•
Some general procedrures for homogeneity assessment and
homogenization
A brief review of techniques. Will briefly introduce these methods (not
necessarily in this order)
–
–
–
–
–
–
–
•
What does homogeneous (and inhomogeneous) mean?
Why a time series may become inhomogeneous
What does homogeneity assessment mean?
What does homogenization mean?
How does the lack of homogeneity compromise climate analysis?
Craddock + Metadata
Likelihood ratio: SNHT
Regression models
Two-phase regression
Caussinus-Mestre
Vincent’s interpolation of daily factors
Della Marta and Wanner
The HOME-COST Action
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
A FEW QUESTIONS TO START
• What does homogeneous mean?
– From. lat. homogenĕus, and from gr. ὁμογενής 
“of the same nature”
– Translating the term to climate time series:
• A homogeneous climate time series is defined as one where
variations are caused only by variations in climate. If a long-term
time series is homogeneous, then all variability and change is due
to the behavior of the climate system (WMO TD-1186)
• Conversely, inhomogeneous time series are those presenting any
kind of bias, which impacts the recorded values and is not strictly
caused by true climatic variability and change
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
A FEW QUESTIONS TO START
• Why a time series may become inhomogeneous?
– Because a change has been applied or an error has been
introduced into the conditions the data are measured, recorded,
transmitted, stored and or analyzed resulting in a systematic bias
of a particular segment of the time series
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
A FEW QUESTIONS TO START
• Why a time series may become inhomogeneous?.
Example I: errors in temperature units leading to an artificial change
in variance
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
A FEW QUESTIONS TO START
• Why a time series may become inhomogeneous?.
Example II: change of rain gauge exposure, leading to an artificial
bias in precipitation amount
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
A FEW QUESTIONS TO START
• Why a time series may become inhomogeneous?.
Example III: changes in the way of computing the daily mean
temperature, leading to important biases when compared to WMO
standard (max+min)/2
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
A FEW QUESTIONS TO START
• Why a time series may become inhomogeneous?.
Example IV: impact of urbanization on temperature series, leading to
an artificial enhancement of trends
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
A FEW QUESTIONS TO START
• Why a time series may become inhomogeneous?.
Example V: instrument replacement, leading to an artificial bias
(jump) on radiation series
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
A FEW QUESTIONS TO START
• Why a time series may become inhomogeneous?.
Example VI: impact of relocations and changes in environment on
wind speed time series
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
A FEW QUESTIONS TO START
• Why a time series may become inhomogeneous?.
Example VII: changes in screen type, leading to an artificial bias in
temperature
1.0
0.5
0.0
-0.5
-1.0
-1.5
-2.0
Differences between Simoultaneous temperatures measured in Murcia (Spain). Lines
are Stevenson – Montsouris screen. Red is Tmax (much larger temperatures in
Montsouris screen lead to negative differences); blue is Tmin (slightly larger values in
stevenson screen lead to positive differences); green is Tmean, which balances the
effect of Tmax and Tmin into negative differences (i.e. larger temperatures registerd
on ancient screens)
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
A FEW QUESTIONS TO START
• What does homogeneity assessment mean?
– To learn if a time series is or is not homogeneous (I)
Peterson et al, 2002
Aguilar et al, 2005
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
A FEW QUESTIONS TO START
• What does homogeneity assessment mean?
– To learn if a time series is or is not homogeneous (II)
3
2
Quebec – reference series
°C
1
0
-1
-2
-3
1890
1900
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000
Year
Source: Lucie Vincent
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
A FEW QUESTIONS TO START
• What does homogenization mean?
Apply statistical techniques to transform a) into b) and try to
eliminate as much as possible non climatic influences biasing the
time series
b) Quebec City, 1895-2002
(Non adjusted)
4
4
3
3
2
2
1
1
°C
°C
a) Quebec City, 1895-2002
(Non adjusted)
0
0
-1
-1
-2
-2
-3
-3
-4
1890
-4
1890
1900
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000
1900
1910
1920
1930
1940
1950
1960
1970
1980
Year
Year
Source: Lucie Vincent.
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
1990
2000
A FEW QUESTIONS TO START
• How does the lack of homogeneity compromise climate analysis?
Quebec City, 1895-2002
4
3
2
Trend before homogenization:
-0.7°C in 106 years
°C
1
0
-1
-2
-3
-4
1890
1900
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000
Year
Source: Lucie Vincent.
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
A FEW QUESTIONS TO START
• How does the lack of homogeneity compromise climate analysis?
Quebec City, 1895-2002
4
3
2
°C
1
0
Trend after homogenization:
-1
+2.1 °C in 106 years
-2
-3
-4
1890
1900
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000
Year
Source: Lucie Vincent.
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
SOME GENERAL QUESTIONS
Use Quality Controlled Data
Detect inhomogeneities
(in other words, identify
homogeneous subperiods)
Adjust to the last homogeneous subperiod
Validate results
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
A GENERAL PROCEDURE FOR HOMOGENEITY
ASSESSMENT AND HOMOGENIZATION
Metadata
Detect inhomogeneities
(in other words, identify
homogeneous subperiods)
Visual inspection
Test
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
SOME GENERAL QUESTIONS
Test
-Identify if period A is
different from period B
(good when you have
reliable metadata)
- Identify in which data
point the time series is
most likely to have
breakpoint
- Iterate over the series or
use a model that allows
multiple breaks detection
Over the data?
Climate fluctuations may be
confused with inhomogeneities
Using reference series?
Using a model based on a reference
series or running the test with the help
of a reference series should help to
distinguish climate effects from true
inhomogeneities
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
ON THE USE OF REFERENCE SERIES
Using reference series?
-Decorrelation (network
density)
-Homogeneity of the reference
series
- Specially problematic at early stages (i.e. 19th
century), due the lack of data
Auer et al, 2005
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
THERE IS A MULTIPLICITY OF TESTS
AVAILABLE
• Simple (but elaborated!) formulatations  Craddock Test
+ Metadata
• Caussinus-Mestre
• Likelihood ratio tests  SNHT and variants
• Regression model tests  Vincent
• Two Phase Regression  Wang
• MASH  will be discused later on by T. Szentimrey
• For introductory explanations on these and other
methods, see Aguilar et al (2003)*: Guidance on
Metadata and Homogenization, WMO-TD-1186.
• *: This is almost 5 years old… see later on slides on
COST-HOME action!
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
ON THE APLICATION OF THE CRADDOCK
TESTS
• Auer et al (2007)and many others apply the Craddock Test to
climatological data
• The test has a simple formulation and HISTALP heavily relies on
metadata and expertise to identify/confirm/reject potential breaks
• It accumulates the normalized differences between two series (a
and b) according to one of the following formulas:
s n  s n 1  a n  (bm  a m )  bn
(4A)
bm
sn  sn1  an
 bn
am
(4B)
• Where: s is the sum at the current obs; s-1 the sum at the previous
obs; an is the obs at the candidate station; am is the mean of the
candidate station; bn is the obs at the reference station; bm is the
mean of the reference station
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
From Maugheri, M.
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
News about a damage to the pluviometer.
In corrispondence with repairing the
damage, the cause of the underestimation of
precipitation has been removed for the
period 1900-1928
Craddock test - Bologna precipitation record
“All’inizio del 1857 a questo pluviometro,
6000
ridotto in cattivo stato pel lungo uso, ne venne
sostituito un altro di migliore costruzione, e
lavorato con
5000molta precisione...”
4000
3000
2000
1000
0
Change in data origin: from “Osservatorio
Astronomico” to “Istituto Idrografico”
-1000
-2000
Introduction of a new pluviometer (Fuess
recorder): “... fu collocato a cura del prof
Bernardo Dessau nel periodo 1900-1903 ...”
-3000
From Maugheri, M.
-4000
-5000
CRADD-FER
CRADD-PAD
CRADD-VAL
CRADD-PAR
CRADD-FIR
CRADD-REM
CRADD-ARE
CRADD-MAN
CRADD-PIA
CRADD-ROV
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
2000
1995
1990
1985
1980
1975
1970
1965
1960
1955
1950
1945
1940
1935
1930
1925
1920
1915
1910
1905
1900
1895
1890
1885
1880
1875
1870
1865
1860
1855
1850
1845
1840
1835
1830
1825
1820
1815
1810
-6000
ON THE APPLICATION OF CRADDOCK
TEST (generalizable to homogeneity work)
• Auer et al (2007) say:
– For the nucleus of homogeneity testing (the comparison of two series)
we use Craddock’s normalised accumulated difference/ ratio series
(Craddock, 1979), although HOCLIS would allow any method of
relative homogeneity testing to be used. The practical experience in
our group with a number of such methods tells us that the rejection of
break signals due to statistical non-significance (as provided by
higher developed methods) is often misleading. Strong breaks may
remain in the series simply owing to the fact that the typical length of a
homogeneous subinterval (Table I) is short in relation to interannual
variability. We try to compensate for the deficits of our method in
pure statistical terms by investing much work into metadata
analysis, which we regard as the ultimate measure to decide whether a
break can be accepted or not.
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
ON THE APPLICATION OF
CRADDOCK TEST
1. Ignore any previous homogeneity work undertaken for any of the series (i.e. start from the beginning,
assuming all series contain potential breaks).
2. Test in small, well-correlated subregions (a maximum of 10 series tested against each other results in a
10 × 10 decision matrix, which enables most breaks detected to be assigned to a most likely candidate
series).
3. Choose the most appropriate reference series with a non-affected subinterval for the adjustment of
each break detected (i.e. different reference series can be used for each break detected in a candidate
series).
4. Avoid erratic monthly precipitation adjustments by smoothing the annual course of adjustment factors.
5. Detect outliers and ‘overshooting adjustments’ using spatial comparisons (by mapping precipitation
values both in absolute and relative units) for each month of the study period.
6. Attempt to determine support for homogeneity adjustments when few metadata are available (i.e.
contact data providers for more information in difficult cases).
Auer et al
(2005)
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
LIKELIHOOD RATIO TESTS:
THE STANDARD NORMAL HOMOGENEITY
TEST AND VARIANTS
• Formulated by Alexandersson (1986) and Alexandersson
et al (1997)
• Critical values derived after MCS
• Recently Khaliq and Ouarda have recalculated the
critical values using improved MCS
• Widely re-formulated (for example, Reeves et al, 2006)
• Widely applied (will see example by CCRG)
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
SHNT
Original Data
Reference Series
k
år
j 1
2
j
( y j  ( X  Y j ))
å
k
j 1
r2 j
q-series (data-reference)
z-series
(standarized q-series)
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
SNHT
Most Probable Breakpoint: Max of
Correction Factor:
T j  jz12  (n  j) z22
f  q2  q1
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
SNHT MODIFICATIONS
BY REEVES et al (2007)
• The standarization into z series proposed by
Alexandersson :
• Uses s to estimate the standard deviation of the series,
which might be ineficient if the candidate series is
inhomogeneous
• They propose to avoid standarization by using:
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
A HOMOGENIZATION PROCEDURE BASED
ON THE SNHT TEST (AND OTHER
METHODS)
QCd daily data of TMax
and TMin
Calculation of Monthly Values of
TMax and TMin
Blind break-point detection over annual,
seasonal TMax, Tmin, Tmean with
automated SNHT (1997)
Screen Bias Minimisation
over monthly series of
TMax and TMin
Breakpoint validation (metadata, plot checks, …)
Monthly,
Seasonal, Annual
Tmax, Tmin, DTR,
TMean Series
(STS)
Application to
monthly Tmax and
Tmin (As described
in Aguilar et al, 2002)
Interpolation to daily data
(Vincent et al., 2002)
Validation of
daily corrected
values
Generation of correction pattern
SDTS
Aguilar, E., Brunet, M., Saladié, O., Sigró, J. : Homogenization of the Spanish Daily Temperature Series. A step forward.
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
SCREEN BIAS MINIMIZATION
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
SCREEN BIAS MINIMIZATION
Large effect on
TMax
Much smaller
effect on TMin
CCRG’s SCREEN project (CICYT)  2 replicas of Montsouris Screen,
on operation since 2003
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
SCREEN BIAS MINIMIZATION
3,00
40,0
2,00
Montsouris-Stevenson
Tmaxstev mur
30,0
20,0
10,0
1,00
0,00
10,00
20,00
30,00
Tmaxmont mur
40,00
10,00
20,00
30,00
40,00
Montsouris TMax
Murcia: TMaxStev = -0.508 + TMaxMont*0.975
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
SCREEN BIAS MINIMIZATION
Tmax data for Murcia
(August)
Red: Murcia Original
Green: Murcia
Screen-Corrected
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
BREAK POINT DETECTION
BLIND RUN OF AUTOMATED SNHT (see ALEXANDERSON
ET AL., 1997) OVER ANNUAL AND SEASONAL VALUES OF
TMAX, TMIN, TMEAN AND DTR
Original Data
Reference Series
k
år
j 1
2
j
( y j  ( X  Y j ))
å
k
j 1
r2 j
q-series (data-reference)
z-series
(standarized q-series)
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
BREAK POINT DETECTION
BLIND RUN OF AUTOMATED SNHT (see ALEXANDERSON
ET AL., 1997) OVER ANNUAL AND SEASONAL VALUES OF
TMAX, TMIN, TMEAN AND DTR
Most Probable Breakpoint: Max of
Correction Factor:
T j  jz12  (n  j) z22
f  q2  q1
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
BREAK POINT DETECTION
INITIAL PHASE
SESION 1
SESION 2
Series
Series
Series
Series
Series
...
Series
Series
Series
Series
Series
Series
...
Series
A1
B1
C1
D1
E1
X1
A2
B2
C2
D2
E2
Iteration
until no
more
breakpoints
are found
X2
SESION n
Series
Series
Series
Series
Series
...
Series
An
Bn
Cn
Dn
En
Xn
FINAL PHASE
SESION 1
Series
Series
Series
Series
Series
...
Series
A1
B1
C1
D1
E1
X1
An ... Xn
are used as
references
HOMOGENEOUS SERIES
Series Ah
Series Bh
Series Ch
Series Dh
Series Eh
...
Series Xh
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
BREAK POINT VALIDATION
Green: number of references
Red: z-series
Tm Detection
03 17 1955 -1.89
Tn Detection
03 17 1914 5.51
03 17 1954 -2.58
03 17 1935 2.16
Tx Detection
03 17 1970 2.54
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
CORRECTION PATERN
In 1954 station was relocated from the city center to the airport
Green: number of references
Red: z-series
Period: 1880-2006
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
CORRECTION RESULTS OVER
ANNUAL TMean (BADAJOZ)
Original
Corrected
Red: original; green: corrected
(Screen +SNHT)
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
APPLICATION TO MONTHLY SERIES
BADAJOZ, TMax
Factors for 1954 Breakpoint. Tmax, Badajoz Observatorio to Villafría
Month
StartYear BreakPoint
EndYear
Factor
14
1
1876
1954
2005
-2.382
2
1876
1954
2005
-1.826
3
1876
1954
2005
6.681
10
4
1876
1954
2005
7.811
8
5
1876
1954
2005
11.461
6
1876
1954
2005
10.319
7
1876
1954
2005
7.4
4
8
1876
1954
2005
8.285
2
9
1876
1954
2005
12.457
10
1876
1954
2005
4.099
0
11
1876
1954
2005
3.498
-2
12
1876
1954
2005
0.996
12
6
1
2
3
4
5
6
7
8
6
7
8
9
10
11
12
9
10
11
12
-4
Factors for Trend Removal. Badajoz "Observatorio"
Month
StartYear
Endyear
0.1
Factor
1
1909
1954
0.059
2
1909
1954
-0.017
3
1909
1954
-0.22
4
1909
1954
-0.238
5
1909
1954
-0.308
6
1909
1954
-0.311
7
1909
1954
-0.266
8
1909
1954
-0.355
9
1909
1954
-0.438
10
1909
1954
-0.166
11
1909
1954
-0.113
12
1910
1954
0.016
0
1
-0.1
-0.2
2
3
4
5
All Values in
1/10th of ºC
-0.3
-0.4
-0.5
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
ADJUSTMENT OF MONTHLY SERIES
August TX
January TX
Red: original; green: adjusted
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
CONVERTING MONTHLY
FACTORS TO DAILY FACTORS
Following Vincent et al. (2002),
monthly factors are assigned to the
15th of each month to avoid abrupt
discontinuities at the end of the month
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
CLIMATE CHANGE INDICES DERIVED
FROM DAILY TIME SERIES
Badajoz,
TX90p índex
Red: oiginal
Green: corrected
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
CLIMATE CHANGE INDICES DERIVED
FROM DAILY TIME SERIES
Badajoz,
TX10p índex
Red: oiginal
Green: corrected
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
CLIMATE CHANGE INDICES DERIVED FROM DAILY TIME
SERIES
Badajoz,
TN90p índex
Red: oiginal
Green: corrected
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
CLIMATE CHANGE INDICES DERIVED FROM DAILY TIME
SERIES
Badajoz,
TN10p índex
Red: oiginal
Green: corrected
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
CAUSSINUS and MESTRE (2004)
•
Use a fairly more complicated penalized log-likelihood procedure to correct
groups of stations sharing the same climate signal
•
C-M assume that each series is the sum of climate effect, a station effect
and a random white noise. The station effect is constant if the series is
reliable (homogeneous). If not, the station effect is piecewise constant
between two shifts (except for outliers)
The maximization of the statistic, and thus the model selection, implies
testing a far too large number of combinations of break-points and oultiers
positions
•
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
CAUSSINUS and MESTRE (2004)
• For practical application, pair-wise comparisons across the
neighbours are performed by calculating difference series and the
arising breaks/outliers are selected over a decission table.
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
CAUSSINUS and MESTRE (2004)
•
•
•
Expertise and metadata records are used again to decide which break points are
retained to be preliminary corrected with a simplified two factors model.
Peliminary corrected data is submitted again to pairwise comparison to ensure that
no important breakpoints were left untreated and to benefit of the corrections applied
to other stations
Once all beakpoints and outliers are known for all the stations, the full model is run
¡
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
A MORE SOFISTICATED MODEL FOR
ADJUSTING DAILY TEMPERATURE DATA:
DELLA-MARTA and WANNER (2006)
•
Defined their method in 10 steps:
1. Define HSPs for the candidate and as reference stations as
possible (this method does not provide its own detection tool)
2. Starting from the most recent inhomogeneity find a reference
station which is highly correlated and has HSP that adequately
overlaps both HSP1 and HSP2 of the candidate station
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
A MORE SOFISTICATED MODEL FOR
ADJUSTING DAILY TEMPERATURE DATA:
DELLA-MARTA and WANNER (2006)
3. Model the relationships
between the paired
candidate and reference
observations before the
inhomogeneity (i.e. in the
period of common
overlapping within HSP1 of
the candidate, 1988-2003
for Graz-Uni, using Wien)
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
A MORE SOFISTICATED MODEL FOR
ADJUSTING DAILY TEMPERATURE DATA:
DELLA-MARTA and WANNER (2006)
4. Predict the temperature at
the candidate station after
the inhomogeneity using
observations from the
reference and the
previously obtained model
5. Create a paired difference
series between the
predicted and the observed
model within HSP2
6. Find the probability
distribution of the candidate
station in HSP1 and HSP2
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
A MORE SOFISTICATED MODEL FOR ADJUSTING
DAILY TEMPERATURE DATA:
DELLA-MARTA and WANNER (2006)
7. Bin each temperature
difference in the difference
series (step 5), according to
its’ associated predicted
temperature, in a decile of the
probability distribution of the
candidate station at HSP1
8. Fit a smoothly varying function
between the binned decile
differences (step 7) to obtain
an estimated adjustment for
each percentile
9. Unsing the probability
distribution of the candidate in
HSP2 (step 5) determine the
percentile of each observation
in HSP2 and ajust by the
amount calculated in step 8
10. Proceed to the remaining
HSPs
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
A MORE SOFISTICATED MODEL FOR ADJUSTING
DAILY TEMPERATURE DATA:
DELLA-MARTA and WANNER (2006)
Results
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
A MORE SOFISTICATED MODEL FOR ADJUSTING
DAILY TEMPERATURE DATA:
DELLA-MARTA and WANNER (2006)
Comparisons
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
REGRESSION MODEL TESTS 
VINCENT’S TEST
• Vincent, in 1998, described a new approach based on
the fitting of a hierarchy of regression based models to a
time series an the analysis of the residuals
• The model has been, as well as SNHT, widely applied
and many variants have appeared
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
VINCENT’S TEST
-A visual inspection of the plots
may tell enough to infer whether
the series is homogeneous (top,
model accepted, process finished),
has an artificial trend (left) or an
artificial jump (closer plot)
- The Durbin-Watson statistics and
the analysis of the correlogram are
use to take the final decision
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
VINCENT’S TEST
Iteration throguh all possible p
changepoints. When
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
VINCENT’S TEST
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
REGRESSION MODEL TESTS 
VINCENT AND VARIANTS
Reeves et al (2007) describe as follows Vincent’s procedure
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
TWO PHASE REGRESSION
• Another widely used
family of methods are
those based on two
phase regressoin.
• With pioner
applications by Solow
(1987) and Peterson
and Easterling (1995)
and reformulated by
Lund and Reeves
(2002)
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
RH-TEST
•
•
•
•
Wang (2003) defines the following
model with commond trend
RH-Test is a software package
base in an improved version of the
former model, widely used at
WMO-CCl-ETCCDI workshops
and in many other publications
Includes an iterative procedure to
detect multiple breakpoints and
the new statistics account for
important aspects as serial
autocorrelation
Available at:
http://cccma.seos.uvic.ca/ETCCD
MI/software.shtml
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
WHICH IS THE BEST METHOD?
•
•
•
There is no agreement
There is a sense that MANY methods work well (specially for detection on
annual to monthly) if they are applied with care and expertise
Many authors have performed statistical comparisons:
–
–
–
–
•
Ducré et al (2003)
De Gaetano (2005)
Reeves et al (2007)
...
Comparisons (as well as all homogeneity work) depend on several things
–
–
–
–
The tested data
The test application procedures
The software used
Which quality do we prefer (false detection, false negatives, position, magnitude
of the break)
– …
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
WHICH IS THE BEST METHOD?
From Ducré-Robitaille et al
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
WHICH IS THE BEST METHOD?
From Ducré-Robitaille et al (2003)
False detection magnitude and positions over 1000 simultaed series
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
COST ACTION HOME.
Scientific Activities
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
COST ACTION HOME.
Working Groups
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
FINAL MESSAGE
The method is important; its application, even more
i.e.: the best method in bad hands
will do less a worst method in good hands
BEST SCENARIO: good method, good hands.
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007
• Thank you!
SUMMER SCHOOL ON THE PREPARATION OF CLIMATE ATLAS Sitke (Hungary); 10 - 14 September 2007