Wavelet - Bootstrap based Multiple linear regression models for flood forecasting in Mahanadi basin. - Vinit Sehgal Under The guidance of: 4 th year UG Student Dr. C. Chatterjee Department Of Civil Engineering Agril. & Food Engg. Department Birla Institute of Technology Indian Institute of Technology Mesra, Ranchi Kharagpur
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Wavelet bootstrap Multiple linear regression models
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Wavelet - Bootstrap based Multiple
linear regression models for flood
forecasting in Mahanadi basin.
- Vinit Sehgal Under The guidance of:
4th year UG Student Dr. C. ChatterjeeDepartment Of Civil Engineering Agril. & Food Engg. Department
Birla Institute of Technology Indian Institute of Technology
Mesra, Ranchi Kharagpur
Problem statement
• The aim of the study was to
(a) develop accurate and reliable models for daily discharge forecasting
based on Wavelet and bootstrap soft computing techniques using the
minimum possible data and
(b) to compare the results with the previous studies on the Mahanadi basin.
I
Catchment area and
Selection of Data• Data sets for seven stations of Mahanadi basins were
hata and Hirakud dam which are shown in the figure.
• A correlation study was carried out to investigate the usefulness of the
stations data for model formation.
• It was seen that Tikampara and Hirakud dam release had maximum
correlation with the data at Naraj. Correlation of the 6 stations with the data
at Naraj is given in the following table.
Station Correlation with Naraj
Khairmal 0.71
Hirakud 0.83
Salebhata 0.48
Kesinga 0.47
Kantamal 0.49
Tikarpara 0.93
• Only discharge at Tikampara and Hirakud release were found to be in good
correlation with the discharge at Naraj.
• Further correlation analysis showed that keeping other stations in the
model formation wont help improve the results (results not shown).
• The correlation study was extended further to decide the significant
antecedent time series from each station in the formation of models.
Input combinations v/s correlation
with discharge at Naraj
This establishes that antecedent data of Naraj till (t-6), Tikampara and
Hirakud till (t-3) will make significant inputs.
II
Selection of Wavelet for DWT
• Selection of wavelets if an important factor on which the performance of
wavelet based models depend.
• Wavelets with high vanishing moments are believed to be more sensitive
towards high frequencies, and hence, are more suitable for application in
hydrological forecasting problems.
• A novel study was carried out in which wavelet based simple MLR models
were formed using 17 wavelets of various families to forecast 1- day ahead
discharge at Naraj using the DWC’s of the significant inputs as described
in slide 6 and the results were tabulated as follows.
Wavelet Vanishing Moment E (%) RMSE MAE CC
bior 1.1 1 92.65 2351.84 1683.35 0.9652
haar 1 93.53 2206.78 1532.48 0.9682
coif1 2 93.53 2206.78 1532.48 0.9682
db2 2 96.62 1594.07 1199.33 0.983
bior 3.3 3 97.27 1431.57 1104.63 0.9863
db 5 5 97.81 1283.15 959.78 0.989
coif3 6 98.83 935.53 758.15 0.9944
bior 6.8 6 99.15 799.58 610.037 0.9958
db 10 10 99.24 756.27 578.13 0.9963
coif5 10 99.5 609.23 482.82 0.9975
db 15 15 99.65 507.16 422.11 0.9982
db 20 20 99.67 494.3 373.41 0.998
db 25 25 99.74 441.64 362.32 0.9987
db 30 30 99.78 406.49 337.12 0.9989
db 35 35 99.79 397.42 318.41 0.9989
db 40 40 99.81 370.39 307.38 0.9991
db 45 45 99.81 377.58 313.18 0.999
No. of vanishing moments of a wavelet v/s performance of models
Conclusion on selection of wavelet for DWT
• It was served that the wavelets from db family performed better than other
family wavelets as they have maximum vanishing moments for a given
support width of a wavelet.
• Greater the vanishing moment of the wavelet used for DWT, better is the
performance of wavelet based models.
• Hence db 45 was considered to be the best wavelet for the model
formation.
Discrete wavelet components of the discharge series of Naraj
for the year 2000- 05. (upto 3 resolution levels)
III
Wavelet- Bootstrap Model formation and performance analysis
• After the significant inputs were decomposed upto 3 levels using db 45 wavelet, these DWC’s were used in the formation of models instead of the original time series.