1. Statistical downscaling of GCM outputs using wavelets based models
Anchit Lakhanpal
Vinit Sehgal
Under the supervision of
Dr. Rakesh Khosa
Professor
Dr. R. Maheswaran Inspire Faculty
Department of Civil Engineering
Indian Institute of Technology (IIT) Delhi

2. OBJECTIVES OF STUDY
Statistical downscaling of GCM outputs by wavelet based models using Wavelets for Krishna basin both for precipitation and temperature.
Future extreme events modeling
Comparison of models

3. GCM
General Circulation Models (GCM)
Future Scenarios
Impact on Water Resources
Mathematical models developed by considering physics involved in land, ocean and atmospheric processes in form of a set of linear and non linear partial differential equations.
Available at coarse grid size of 300Kms.
Project climatic variables globally at coarse resolution.

4. Need of Downscaling
Differences between the real world and its global model representation.
GCM’s do not incorporate sub-grid features such as topography, land surface process, land use pattern and cloud physics.
Poor representation of factors, affecting local climate.
Bridges mismatch of spatial scale between the scale of GCM’s and the resolution needed for impact assessments.

6. Statistical downscaling
Downscaling methods
Statistical downscaling
Dynamic downscaling
Data driven approach deriving empirical relationship that transform large scale features of GCM simulated climatic variables in to regional scale variables
Uses statistical relationships(regression equations) where fine scale predictands is related to set of coarse – resolution predictors
Morkov models, ANN,KNN,SVM Clustering techniques, Baysein joint probability
Uses physically based models with finer space resolution than the original global model
Takes input from GCM simulation as initial and boundary conditions and takes in to account sub-grid features and produce high resolution results.
Computationally expensive and complicated
HadRM3H, PRECIS, COSMO-CLM, RegCM3

7. Study region
Catchment of Krishna River extends over Maharashtra Karnataka ,Andhra Pradesh and Telangana,
total area of 2,58,948 Sq.km which is nearly 8% of the total geographical area of the country.
situated between:
19˚N and 23.7˚N latitude
80.4˚E and 86.9˚E longitude.
Length of Krishna River (Km) :1400

8. Probable Atmospheric Variables
S.no
Predictor
Pressure levels (mb) 1
Atmospheric Temperature
1000, 925, 850, 700, 600, 500, 400, 300, 250, 200, 150, 100, 70, 50, 30, 20, 10 2
Eastward Wind 3
Northward Wind 4
Geo-potential Height 5
Sea Level Pressure 6
Surface Temperature

9. PCA & WAVELET DECOMPOSTION
NCEP ( )
VARIABLE AVERAGING
PCA & WAVELET DECOMPOSTION
MODELING
MLR
STANDARDISATION
GCM ( )
RCP4.5

10. Selection of variables
Data should be available for desired period
Selected GCM should be capable of simulating variable well
Predictor must show good relation with predictand
A predictor may not be significant for present climate but may become key predictor for future

11. Variable Averaging- PSL

12. Variable Averaging- ZG

13. Variable Averaging- TA

14. Principal Component Analysis
PCA is applied to data in which orthogonal transformation is applied on set of correlated predictor variables producing principal components
Principal components are dimensionally reduced and uncorrelated to one another i.e. reduces dimensionality and multicolinearity
These components carries almost the same variability as that of the original data

15. Wavelets
Multiresolution analysis(MRA) is carried to study various frequencies at various resolutions or scales using variable window size.
Simultaneous localization of frequency and time.
Since most of the natural time series are discrete in nature, Discrete Wavelet Transform is applied for decomposition and reconstruction of time series.

16. Animation showing scaled and translated wavelet (window) on a given signal

17. Discrete Wavelet Transform (DWT)
To localize the frequency and time, signal need to be decomposed at various levels using the low pass and high pass filters.
The original time series is decomposed through a process consisting of a number of successive filtering steps giving
a) Approximation(Low frequency terms)
b) Details(High frequency terms)

18. Decomposed time series up to level 3

19. Precipitation POINT MLR W-MLR IMPROVEMENT(%)
WAVELETS BASED MODELS OUTPERFORM STAND ALONE MODELS IN CAPTURING PEAKS BY(%) A
0.764
0.786
2.93
65.22 B
0.893
0.9
0.79
61.9 C
0.709
0.745
5.03
57.14 D
0.733
0.756
3.11 80 E
0.588
0.696
18.47 75

20. Precipitation Point-B

21. Future Precipitation (Point B)

22. Temperature POINT MLR W-MLR IMPROVEMENT(%)
WAVELETS BASED MODELS OUTPERFORM STAND ALONE MODELS IN CAPTURING PEAKS BY(%) A
0.902
0.932
3.3
73.91 B
0.915
0.928
1.42
54.17 C
0.944
0.961
1.78
70.83 D
0.949
0.959
1.11 80 E
0.924
0.953
3.13 75

23. Temperature (PointB)

24. Future Temperature (PointB)

25. Conclusion
Wavelet based models are superior than stand alone models in capturing the extreme events at all the points.
Both precipitation and temperature are downscaled to desired scale to capture modeling variance in climatic time series.
However we observe that the accuracy of models for precipitation is significantly lower than that of temperature. Hence we need to revisit the problem with non- linear approaches to be able to model the process better.

26. Appendix

27. Appendix 1: LITERATURE REVIEW
Majumdar.P.P, et al.
2007
Statistical methodology involves principal component analysis, fuzzy clustering and RVM to model stream flow at river basin scale using GCM simulated climatic variables.
Hessami. Masoud , et al.
Automated regression-based statistical downscaling tool on Canadian Coupled GCM (CGCM1) and Hadley Centre Climate Model (HadCM3) and their comparison.
Anandhi.A,
et al.
Presents a methodology to downscale monthly precipitation to Malaprabha river basin using Support Vector Machine (SVM). Separate downscaling model is developed for each season to capture the relationship between the predictor variables and the predictand.

28. Hua. C, et al.
2008
Smooth Support Vector Machine (SSVM) method was constructed to predict daily precipitation of the changed climate in the Hanjiang Basin. In SSVM, smoothing techniques are applied to solve important mathematical programming problems
Cai, X. et al.
2009
No GCM is superior in predicting temperature or precipitation for the whole world, although some GCMs score better in particular regions). The performance of GCMs is assessed according to their ‘‘skill scores’’
Ghosh.Subimal, et al.
2013
High-resolution multisite daily rainfall projections in India
with statistical downscaling for climate change impacts assessment. Use of statistical downscaling model classification and regression tree, and kernel Regression.

29. Appendix 2: Data Description
GCM
CanCM4 (AR5, IPCC), grid size 2.8° X 2.8 Canadian Centre for Climate Modelling and Analysis
Historical( )
RCP 4.5 scenario ( )
NCEP/NCAR
National Centre for environmental Prediction, grid size 2.5° X 2.5° Reanalysis data ( )
IMD
Indian Meteorological Department grid size 0.5° X 0.5° ( )

30. Appendix 3: GCM future scenario
In AR5 four Representative Concentration Pathways (RCPs) were selected and defined by their total radiative forcing (cumulative measure of human emissions of GHGs from all sources expressed in Watts per square meter) pathway and level by 2100.
RCP4.5 represents stabilization without overshoot pathway to 4.5 W/m2 at stabilization after 2100

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33. Links
data.org/sim/gcm_monthly/AR5/Reference-Archive.html
.reanalysis.html

34. THANK YOU