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A Statistical DownScaling
Model (SDSM) Primer
Dr Rob Wilby
King’s College London
Presentation outline
• A brief reminder
• The Statistical DownScaling Model (SDSM)
• Overview of software structure and data archive
• Main functions of SDSM
• A few cautionary remarks
What impacts modellers need…...
Point
1m
10km
50km
300km
What climate modellers supply…...
Statistical DownScaling Model
Precipitation occurrence
An nth order, two state process governs daily
precipitation occurrence, with serially independent
precipitation amounts on wet days
π t = xβ + ε
where t is the conditional probability of a wet day, X is
a K1 vector of standard Gaussian (i.e., normally
distributed, with zero mean and unit variance)
explanatory variables,  is the coefficient matrix, and 
is random noise.
Precipitation occurrence (cont.)
The binary event of precipitation, Pt or no precipitation
is determined by
Pt = {
1,
if utt
0,
otherwise
where ut denotes uniform independent random forcing
for the occurrence process (probability density f[u] =1,
0 u 1).
Notes:
• Autocorrelation is incorporated implicitly by predictors
• Separate equations may be specified for each month
Conditional variables
Conditional variables, including nonzero precipitation
amounts rt are simulated by
rt = zβ + ε
where Z is a K1 vector of standard Gaussian (i.e.,
normally distributed, with zero mean and unit variance)
explanatory variables,  is the coefficient matrix, and 
is an error term which is modelled stochastically (by
assuming zero mean and variance equal to model
standard error).
Conditional variables (cont.)
Many conditional variables (such as nonzero precipitation
amounts and sunshine hours) are strongly skewed to the
right. Therefore, a range of transformations for rt are
available in SDSM, including exponential, fourth root, and
inverse normal (version 2.3 only).
Illustration of the inverse normal transformation
Cumulative probability
ly
Au
gu
Se
st
pt
em
be
r
O
ct
ob
er
N
ov
em
be
D
r
ec
em
be
r
Validation of SDSM (red) wet-day occurrence (%)
1976-1990 compared with observations (blue).
Q95
Q05
Q50
40000
20000
0
01/01/76
0.4
0.2
0
10
100
1000
Validation of SDSM (red) daily precipitation totals
1976-1990 compared with observations (blue).
Precipitation anomaly (%)
CuSum (tenths mm)
60000
0.6
100.00
Observed
80000
0.8
Precipitation total (tenths mm)
120000
100000
1
1
Ju
Ju
ne
ay
M
Ap
r
il
60
55
50
45
40
35
30
25
20
Ja
nu
ar
y
Fe
br
ua
ry
M
ar
ch
Wet-days (%)
Examples of SDSM performance (at Kew)
50.00
0.00
-50.00
-100.00
01/01/79
01/01/82
01/01/85
01/01/88
01/01/91
Validation of SDSM (violet, red, orange) cumulative
precipitation totals (tenths mm) 1976-1990 compared
with observations (blue).
1960
1980
2000
2020
2040
2060
2080
2100
20-day winter maximum precipitation anomalies (%)
for the Eastern England grid-box of HadCM3 (grey)
and for SDSM (red) under the A2 emission scenario.
Structure and data archive
Select
predictand
Quality
control
Station
data
Scatter
plot
Select
predictors
Screen
variables
NCEP
data
(Un)conditional
process?
Set model
structure
Transform
variables
Calibrate
model
Station and
NCEP data
NCEP
predictors
Downscale
predictand
GCM
predictors
Generate
scenario
Weather
generator
Model
output
Analyse
results
Compare
results
Chart
results
Impact
assessment
SDSM climate
scenario generation
SDSM file extensions and definitions
Extension
Explanation
*.DAT
Observed daily predictor and predictand files employed by the
Calibrate and Weather Generator operations (input).
*.PAR
Meta–data and model parameter file produced by the Calibrate
operation (output) and used by the Weather Generator and
Generate Scenario operations (input).
*.SIM
Meta–data produced by the Weather Generator and Generate
Scenario operations (output).
*.OUT
Daily predictand variable file produced by the Weather
Generator and Generate Scenario operations (output).
*.TXT
Summary statistics produced by the Analyse operations (output).
The HadCM3 cells used in the UKSDSM predictor set
SC
NIa
SB
NEb
IR
WA
EE
SWc
SE
aNI
Scotland
Northern Ireland
Scottish Boarders
Northeast England
Ireland
Wales
Eastern England
Southwest England
Southern England
= (SB+IR)/2
bNE = (SB+EE)/2
cSW = (WA+SE)/2
Daily variables held in the UKSDSM data archive
Daily variable
Code
Precipitation
prec
Maximum temperature
tmax
Minimum temperature
tmin
Mean temperature
temp
Mean sea level pressure
mslp
500 hPa geopotential height
p500
850 hPa geopotential height
p850
Near surface relative humidity
rhum
Relative humidity at 500 hPa height
r500
Relative humidity at 850 hPa height
r850
Near surface specific humidity
shum
Geostrophic airflow velocity
**_f
Vorticity
**_z
Zonal velocity component
**_u
Meridional velocity component
**_v
Wind direction
**th
Divergence
**zh
NCEP
1961–2000
×
×
×
×
×
×
×
×
×
×
×
×
×
×
HadCM2
GG
1961–2099
HadCM3
SRES
1961–2099
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
Generic nomenclature
Each file in the archive complies with a generic nomenclature
of the form
[source] [variable] [grid box] . dat
The source is denoted by characters 1–4, the variable name
by characters 5–8, and the grid box code by characters 9–
10. All files have the extension *.dat. For example
nceprhumee.dat
indicates that the source is NCEP [ncep], the variable is near
surface relative humidity [rhum], and the grid box is Eastern
England [ee].
Relationship to UKCIP02 scenarios
SDSM
HadCM3H
1961-1990
2071-2100
Statistical
downscaling
1961-2100
SRES
(A2,B2)
HadCM3
UKCIP02
HadCM3H
1961-1990
2071-2100
HadRM3
1961-1990
2071-2100
Pattern scaling
1990-2100
Baseline climatology
25 variables
station
5km grid
daily
1961-2100
monthly
2020s, 2050s, 2080s
Main functions
SDSM functions
•
•
•
•
•
•
•
Quality control and data transformation
Selection of predictor variables
Model calibration
Weather generation (observed predictors)
Statistical analyses of model output
Graphing model output
Scenario generation (climate model predictors)
Example bar chart
Example line chart
Example scenario output
Cautionary remarks
Please remember
• SDSM provides a parsimonious technique of scenario
construction that complements other methods
• SDSM should not be used uncritically as a “black box” (evaluate
all relationships using independent data)
• Local knowledge is an invaluable source of information when
determining sensible combinations of predictors
• Daily precipitation amount at individual stations is the most
problematic variable to downscale
• The plausibility of all SDSM scenarios depends on the realism of
the climate model forcing
• Try to apply multiple forcing scenarios (via different GCMs,
ensemble members, time–slices, emission pathways, etc.)
http://www.sdsm.org.uk/
http://www.cics.uvic.ca/scenarios/sdsm/select.cgi
Further reading
**
Conway, D., Wilby, R.L. and Jones, P.D. 1996. Precipitation and air flow indices over the British Isles. Climate Research,
7, 169–183.
Hay, L.E., Wilby, R.L. and Leavesley, G.H. 2000. A comparison of delta change and downscaled GCM scenarios for three
mountainous basins in the United States. Journal of the American Water Resources Association, 36, 387–397.
Wilby, R.L. 1998. Statistical downscaling of daily precipitation using daily airflow and seasonal teleconnection indices.
Climate Research, 10, 163–178.
Wilby, R.L. 1997. Nonstationarity in daily precipitation series: implications for GCM downscaling using atmospheric
circulation indices. International Journal of Climatology, 17, 439–454.
Wilby, R.L. and Wigley, T.M.L. 2000. Precipitation predictors for downscaling: observed and General Circulation Model
relationships. International Journal of Climatology, 20, 641–661.
Wilby, R.L. and Wigley, T.M.L. 1997. Downscaling General Circulation Model output: a review of methods and limitations.
Progress in Physical Geography, 21, 530–548.
Wilby, R.L., Conway, D. and Jones, P.D. 2002. Prospects for downscaling seasonal precipitation variability using
conditioned weather generator parameters. Hydrological Processes, in press.
Wilby, R.L., Dawson, C.W. and Barrow, E.M. 2002. SDSM – a decision support tool for the assessment of regional climate
change impacts. Environmental and Modelling Software, 17, 145–157.
Wilby, R.L., Hay, L.E., Gutowski, W.J., Arritt, R.W., Tackle, E.S., Leavesley, G.H. and Clark, M. 2000. Hydrological
responses to dynamically and statistically downscaled General Circulation Model output. Geophysical Research
Letters, 27, 1199–1202.
Wilby, R.L., Hassan, H. and Hanaki, K. 1998. Statistical downscaling of hydrometeorological variables using General
Circulation Model output. Journal of Hydrology, 205, 1–19.
Wilby, R.L., Wigley, T.M.L., Conway, D., Jones, P.D., Hewitson, B.C., Main, J. and Wilks, D.S. 1998. Statistical
downscaling of General Circulation Model output: a comparison of methods. Water Resources Research, 34, 2995–
3008.
Wilks, D.S. and Wilby, R.L. 1999. The weather generation game: a review of stochastic weather models. Progress in
Physical Geography, 23, 329-357.