1. Data for impact modelling in Sweden: Experiences with empirical downscaling and use of weather generator
Deliang Chen
Regional Climate Group
Earth Sciences Centre
Gothenburg University
Sweden
Acknowledgement: Christine Achberger, Cecilia Hellström
Yaoming Liao, Aristita Busuoic, Youmin Chen, Xiaodong Li
Tinghai Ou, Klaus Wyser, Lin Tang and SWECLIM colleagues

2. Outline Statistical versus dynamic downscaling What we did and learnt?
Requirements from the impact community
Our answers to the requirements

3. Main downscaling approaches: Dynamical (higher resolution models) V L U E
Main downscaling approaches:
Dynamical (higher resolution models)
empirical/statistical downscaling processes
statistical/dynamical downscaling processes
Figure courtesy of David Viner, of the UK Climate Impacts LINK Project.
Figure illustrates the complexity of the downscaling process.
For some studies, the simple methods of constructing finer resolution scenarios may not be sufficient and it may be better to user empirical/statistical or statistical/dynamical downscaling techniques to obtain data at the necessary resolution. An alternative is to use information from higher resolution experiments.

4. Dynamic versus statistical downscaling
Dynamic downscaling builds on physically based models for both global and regional scales
Statistical downscaling relies on GCM for large scale and statistical models for regional and/or local scales.
Dynamic downscaling still has problems with today’s climate!
Can deal with nonstandard or difficult (e.g. Sea ice) variables.
Can handle a variety of different scales.
Less problematic with bias (because of data-based).
Fast ->large number of non-time slice scenarios
However, more risky with extrapolations!
Needs extensive data!

5. What did we during last 5 years (SWECLIM time)?
On the dynamic side, a regional climate model (Rossby Center Model), together with two GCMs (HadCM3 and ECHAM4), has been used to get a number of regional (44*44 km) scenarios for Nordic countries;
Successful statistical models have been developed for monthly temperature and precipitation for Swedish stations. These model have been used to create MONTHLY scenarios for a number of GCM and emission scenarios.

6. Circulation is the dominating forcing of interannual and longer scale varabilitities

7. Improved seasonal cycles by downscalings (SD,DD)
Vänersborg, One station in southern Sweden

8. The maximum sea ice over the Baltic can be realistically predicted by a statistical model (Omstedt & Chen, 2002)

9. Future changes based on the statistical downscaling model driven by 17 GCMs from CMIP2 (Chen et al., 2003)

10. Meeting needs of impact community
Usually high spatial resolution (LRA,WG)
Usually high temporal resolution (WG)
Tailoring of information (WG)
Capability for risk analysis and decisionmaking under uncertainty (WG)
Transparency of scenarios
Practical and useful tools (WG)

11. Our answer to the requirements of Impact community: LRA & WG
LRA=Lapse Rate Approach
WG=Weather Generator

12. LRA (local correction based on topography): observation or modelling based
Observation based method uses observations at different sites in the area to determine the topography dependence
Modelling based method uses a high resolution numerical model to simulate meteorological variables at different sites and the results are then used in determining the topography dependence

13. An Example: The temperature stations in Abisko area
Name
St. no.
Latitude (oN)
Longitude (oE)
Height(m)
Nat_no
RITSEM 1
67.73
17.47
521
17792
AKTSE 2
67.15
18.30
530
17874
ALUOKTA 3
67.32
18.88
385
17879
TARFALA 4
67.90
18.62
1140
17897
ÅLLOLUOKTA 5
67.13
19.50
370
17974
NIKKALUOKTA 6
67.85
19.03
470
17995
GÄLLIVARE 7
20.67
365
18073
GÄLLIVARE FLYG. 8
20.83
312
18074
MALMBERGET 9
67.17
373
18075
KIRUNA FLYGPLATS 10
67.82
20.33
459
18094
ABISKO-AUT 11
68.35
18.82
388
18879
ABISKO 12
18880
KATTERJÄKK 13
68.42
18.17
500
18882
RIKSGRÄNSEN 14
68.43
18.13
508
18883
TORNETRÄSK 15
68.22
19.72
393
18976
KATTUVUOMA 16
68.28
19.90
355
18978

14. Lapse rate of temperature

15. The precipitation stations in the area
Name
St. no.
Latitude (oN)
Longitude (oE)
Height(m)
Nat_no
RITSEM 1
67.73
17.47
521
17792
AKTSE 2
67.15
18.30
530
17874
ALUOKTA 3
67.32
18.88
385
17879
ÅLLOLUOKTA 5
67.13
19.50
370
17974
PUOLTSA 6
67.80
19,87
465
17994
NIKKALUOKTA 7
67.85
19.03
470
17995
KAITUM 8
67.53
20.12
490
18001
GÄLLIVARE
20.67
365
18073
MALMBERGET 9
67.17
373
18075
LADNIVAARA 10
67.27
20.27
460
18078
KILLINGI 11
67.52
20.28
485
18086
KIRUNA FLYGPLATS 12
67.82
20.33
459
18094
BJöRKLIDEN 13
68.38
18.68
360
18868
ABISKO 14
68.35
18.82
388
18880
KATTERJÄKK 15
68.42
18.17
500
18882
RIKSGRÄNSEN 16
68.43
18.13
508
18883
BERGFORS 17
68,15
19,80
480
18974
TORNETRÄSK 18
68.22
19.72
393
18976
KATTUVUOMA 19
68.28
19.90
355
18978
KUMMAVUOPIO 20
68.90
20.87
19097

16. Precipitation and height

17. Statistical Downscaling to Enhance Understanding at Local Scales
Source: A Study at the Abisko Laboratory of Net Primary Production under Changing Climate Conditions

18. Ongoing work on WG WG=Stochastic model:basic idea
given slow set of statistics (monthly means and standard deviations, Y, from statistical or dynamical prediction), generate the high frequency variability of the weather (y) based on auto- and cross correlation:
=> y(t) = OT[Y, y(t-1)]
where OT is the time operator.

19. Model calibration (observation)
How a WG works?
Weather Generators
Precipitation Process
Occurrence Amount
Non-precipitation variables
Maximum temperature
Minimum temperature
Solar radiation
Model calibration (observation)
GCM statistics
Of all the climate variables, the precipitation process is most difficult to model and so this is the main process in the model. The other variables are then conditioned on precipitation occurrence.
The precipitation process is split into two - an occurrence process modeling whether precipitation occurs or not, and if it does occur an amount process.
Observed weather data is used to calibrate the model. As is the case with all weather generators, WGEN assumes stationarity, so if there are any trends in the data the model will not perform very well.
Calibration of the model results in the production of a parameter file which is then used to generate synthetic data with the same statistics as the observed data. Comparison of observed and synthetic data is undertaken to check the model performance. If adequate, then the parameter file will then be used as part of climate change studies.
Synthetic data generation
Climate scenarios

20. Other meteorological variables
Condition the statistics of the daily variables (typically maximum/ minimum temperatures and solar radiation) on occurrence of precipitation.
In the classic WGEN model, multiple variables are modelled simultaneously with auto-regression:
Where z(t) are normally distributed values for today’s nonprecipitation variables, z(t-1) are corresponding values for the previous day, and [A] and [B] are K  K matrices of parameters, and (t) is white-noise forcing.

21. Other meteorological variables (cont.)
The z(t) are transformed to weather variables dependent on rainfall occurrence:
if day t is dry
if day t is wet
where each Tk is any of the nonprecipitation variables, k,0 and k,0 are its mean and standard deviation for dry days, and k,1 and k,1 are its mean and standard deviation for wet days.
Seasonal dependence of the means and standard deviations is usually achieved through Fourier harmonics (i.e., sine and cosines).

22. Weather Generators Spatial Downscaling->high spatial resolution!
Calibrate weather generator using area-average weather
Area
Area parameter set
Apply changes in parameters derived from difference between area and grid box parameter sets to individual station parameter files; generate synthetic data for scenario
Calibrate weather generator for each individual station within area
Station parameter set
A stochastic weather generator is a statistical model of observed weather variables, with those variables generally conditioned on the occurrence of precipitation. It is possible to use stochastic weather generators to downscale large-scale climate (Wilks, 1999), by running a weather generator at both the site and area scales.
Wilks, D.S. (1999): Multisite downscaling of daily precipitation with a stochastic weather generator. Climate Research 11,
Calculate changes in parameters from grid box data
Grid Box

23. Generate daily weather data corresponding to the monthly scenario
Temporal Downscaling->high temporal resolution! – Use of monthly scenarios
Weather Generators
Observed station data WG
Parameter file containing statistical characteristics of observed station data
This flow chart from Wilks and Wilby (1999) demonstrates the generation process nicely.
The first step is to generate a uniform random number. If this number is less than or equal to the transition probability currently in effect (this depends on the precipitation status of the previous day) then precipitation occurs. A precipitation amount is then generated based on the gamma distribution, and the transition probability reset to the appropriate value. The wet day non-precipitation parameters are then used to simulate the non-precipitation variables. The process then starts over.
If the random number generated is greater than the transition probability, then a dry day is generated, the transition probability reset to the appropriate value and the dry day parameter set used to simulate the non-precipitation variables. The process then starts over.
Monthly scenario information from GCM, RCM or SD
Generate daily weather data corresponding to the monthly scenario

24. Fundamental Assumption
The statistical correlations between climatic variables derived from observed data are assumed to be valid under a changed climate.
Weather Generators
ADVANTAGES
the ability to generate time series of unlimited length
opportunity to obtain representative weather time series in regions of data sparsity, by interpolating observed parameter data
ability to alter the WG’s parameters in accordance with scenarios of future climate change - changes in variability as well mean changes

25. Weather Generators Challenges
seldom able to describe all aspects of climate accurately, especially persistent events, rare events and decadal- or century-scale variations
designed for use, independently, at individual locations and few account for the spatial correlation of climate

26. A weather generator following Richardson (1981)
P (W |D) = PWD
P (D |D) =PDD= 1-PWD
P (D |W) = PDW
P (W |W) = PWW=1-PDW

27. Daily weather generation (Markov chain)
Not yet!
Daily weather generation (Markov chain)
Source: Wilks and Wilby (1999)

28. PWW
PWD

29. α β

30. A 5 year simulation for Vännesborg

31. Stochastic feature of rain simulation
Daily precipitation at a station
Precipitation (mm)
Date of a month

32. Simulated versus observed monthly precipitation at a Swedish site
Simulation (mm)
Observation (mm)

33. Future
Develop the WG further by including more variables and by testing new formulations such as higher order Markov chain, conditional probability on circulation.
Continue cooperating with DNMI on development and application of the WG in Norway.