multiscale filter methods applied to grace and hydrological data
DESCRIPTION
Multiscale Filter Methods Applied to GRACE and Hydrological Data Willi Freeden, Helga Nutz, Kerstin Wolf. Overview. Motivation Time-Space Analysis Using Tensor Product Wavelets Comparison of GRACE and Hydrological Models (WGHM, H96, LaD) Outlook. Overview. Motivation - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Multiscale Filter Methods Applied to GRACE and Hydrological Data](https://reader035.vdocuments.us/reader035/viewer/2022070411/568147c0550346895db501f6/html5/thumbnails/1.jpg)
Kerstin WolfAG GeomathematikTU Kaiserslautern
GRACE Science Team Meeting 2007:Joined International Symposium:GFZ-Potsdam, 15/-17/10/2007
Multiscale Filter Methods Applied to GRACE and Hydrological Data
Willi Freeden, Helga Nutz, Kerstin Wolf
![Page 2: Multiscale Filter Methods Applied to GRACE and Hydrological Data](https://reader035.vdocuments.us/reader035/viewer/2022070411/568147c0550346895db501f6/html5/thumbnails/2.jpg)
Kerstin WolfAG GeomathematikTU Kaiserslautern
GRACE Science Team Meeting 2007:Joined International Symposium:GFZ-Potsdam, 15/-17/10/2007
Overview
1. Motivation
2. Time-Space Analysis Using Tensor Product Wavelets
3. Comparison of GRACE and Hydrological Models (WGHM, H96, LaD)
4. Outlook
![Page 3: Multiscale Filter Methods Applied to GRACE and Hydrological Data](https://reader035.vdocuments.us/reader035/viewer/2022070411/568147c0550346895db501f6/html5/thumbnails/3.jpg)
Kerstin WolfAG GeomathematikTU Kaiserslautern
GRACE Science Team Meeting 2007:Joined International Symposium:GFZ-Potsdam, 15/-17/10/2007
Overview
1. Motivation
2. Time-Space Analysis Using Tensor Product Wavelets
3. Comparison of GRACE and Hydrological Models (WGHM, H96, LaD)
4. Outlook
![Page 4: Multiscale Filter Methods Applied to GRACE and Hydrological Data](https://reader035.vdocuments.us/reader035/viewer/2022070411/568147c0550346895db501f6/html5/thumbnails/4.jpg)
Kerstin WolfAG GeomathematikTU Kaiserslautern
GRACE Science Team Meeting 2007:Joined International Symposium:GFZ-Potsdam, 15/-17/10/2007
Comparison
1. Motivation
Time Series of Hydrological Models(WGHM, H96, LaD)
Time Series of Satellite Data(GRACE)
Comparative Analysis in Time and Space Domain
All results are computed with data provided from GFZ-Potsdam (1.3)
![Page 5: Multiscale Filter Methods Applied to GRACE and Hydrological Data](https://reader035.vdocuments.us/reader035/viewer/2022070411/568147c0550346895db501f6/html5/thumbnails/5.jpg)
Kerstin WolfAG GeomathematikTU Kaiserslautern
GRACE Science Team Meeting 2007:Joined International Symposium:GFZ-Potsdam, 15/-17/10/2007
Realization of a Time-Space Multiscale Analysisby use of Tensor Product Wavelets
Raw Data:
• Time Series of Spherical Harmonic Coefficients
• Time Series of Water Columns
Determination of Temporally and Spatially Local Changes
Pure and Hybrid Parts
Tensor Wavelet Analysis
Based on Legendre Wavelets in the Time Domain and Spherical Wavelets in the Space Domain
1. Motivation
![Page 6: Multiscale Filter Methods Applied to GRACE and Hydrological Data](https://reader035.vdocuments.us/reader035/viewer/2022070411/568147c0550346895db501f6/html5/thumbnails/6.jpg)
Kerstin WolfAG GeomathematikTU Kaiserslautern
GRACE Science Team Meeting 2007:Joined International Symposium:GFZ-Potsdam, 15/-17/10/2007
Realization of a Time-Space Multiscale Analysisby use of Tensor Product Wavelets
Raw Data:
• Time Series of Spherical Harmonic Coefficients
• Time Series of Water Columns
Determination of Temporally and Spatially Local Changes
Pure and Hybrid Parts
Tensor Wavelet Analysis
Based on Legendre Wavelets in the Time Domain and Spherical Wavelets in the Space Domain
1. Motivation
Why do we apply wavelets?
![Page 7: Multiscale Filter Methods Applied to GRACE and Hydrological Data](https://reader035.vdocuments.us/reader035/viewer/2022070411/568147c0550346895db501f6/html5/thumbnails/7.jpg)
Kerstin WolfAG GeomathematikTU Kaiserslautern
GRACE Science Team Meeting 2007:Joined International Symposium:GFZ-Potsdam, 15/-17/10/2007
SphericalHarmonics
Dirac-Function
Ideal localization in the frequency domain
But: Not any localization in the
space domain
Ideal localization in the space domain
But: Not any localization in the frequency domain
1. Motivation
Uncertainty Principle (in space domain):
![Page 8: Multiscale Filter Methods Applied to GRACE and Hydrological Data](https://reader035.vdocuments.us/reader035/viewer/2022070411/568147c0550346895db501f6/html5/thumbnails/8.jpg)
Kerstin WolfAG GeomathematikTU Kaiserslautern
GRACE Science Team Meeting 2007:Joined International Symposium:GFZ-Potsdam, 15/-17/10/2007
SphericalHarmonics
Dirac-Function
Ideal localization in the space domain
But: Not any localization in the frequency domain
Uncertainty Principle (in space domain):
Solution:
Wavelets
1. Motivation
(Locally) spatial changes only have local influence
Regional changes have an effect on all coefficients
variations of these coefficients cannot be assigned to single regional effects
+
-
Ideal localization in the frequency domain
But: Not any localization in the
space domain
![Page 9: Multiscale Filter Methods Applied to GRACE and Hydrological Data](https://reader035.vdocuments.us/reader035/viewer/2022070411/568147c0550346895db501f6/html5/thumbnails/9.jpg)
Kerstin WolfAG GeomathematikTU Kaiserslautern
GRACE Science Team Meeting 2007:Joined International Symposium:GFZ-Potsdam, 15/-17/10/2007
Overview
1. Motivation
2. Time-Space Analysis Using Tensor Product Wavelets
3. Comparison of GRACE and Hydrological Models (WGHM, H96, LaD)
4. Outlook
![Page 10: Multiscale Filter Methods Applied to GRACE and Hydrological Data](https://reader035.vdocuments.us/reader035/viewer/2022070411/568147c0550346895db501f6/html5/thumbnails/10.jpg)
Kerstin WolfAG GeomathematikTU Kaiserslautern
GRACE Science Team Meeting 2007:Joined International Symposium:GFZ-Potsdam, 15/-17/10/2007
2. Time-Space Analysis
Signal F
Smoothed Part
DetailsFilter Method:
Multiscale Analysis
Filter:Scaling Function
Filter:Wavelets
![Page 11: Multiscale Filter Methods Applied to GRACE and Hydrological Data](https://reader035.vdocuments.us/reader035/viewer/2022070411/568147c0550346895db501f6/html5/thumbnails/11.jpg)
Kerstin WolfAG GeomathematikTU Kaiserslautern
GRACE Science Team Meeting 2007:Joined International Symposium:GFZ-Potsdam, 15/-17/10/2007
Why do we distinguish four parts?connection of temporal and spatial filters via a tensor product:
2. Time-Space Analysis
Multiscale Analysis in Time Multiscale Analysis in Space
smoothing detail smoothing detail
pure hybridsmoothingin time and space
detailin time and space
smoothing in timedetail in space
detail in time smoothing in space
![Page 12: Multiscale Filter Methods Applied to GRACE and Hydrological Data](https://reader035.vdocuments.us/reader035/viewer/2022070411/568147c0550346895db501f6/html5/thumbnails/12.jpg)
Kerstin WolfAG GeomathematikTU Kaiserslautern
GRACE Science Team Meeting 2007:Joined International Symposium:GFZ-Potsdam, 15/-17/10/2007
2. Time-Space Analysis
the higher the scale the finer the details
Graphical Representation of a Multiscale Analysis
Original Signal F
Det
aile
d P
arts
Smoothed Parts
+
+
+
+
+
+
+
+
+
… …
1st Hybrid
2nd Hybrid
Pure
![Page 13: Multiscale Filter Methods Applied to GRACE and Hydrological Data](https://reader035.vdocuments.us/reader035/viewer/2022070411/568147c0550346895db501f6/html5/thumbnails/13.jpg)
Kerstin WolfAG GeomathematikTU Kaiserslautern
GRACE Science Team Meeting 2007:Joined International Symposium:GFZ-Potsdam, 15/-17/10/2007
Waveletsymbol f. scales 2-5 Wavelet f. scales 2-5
2. Time-Space Analysis
Example of a Wavelet Filter: CuP-Wavelet (cubic polynomial)(filter for the detailed information)
![Page 14: Multiscale Filter Methods Applied to GRACE and Hydrological Data](https://reader035.vdocuments.us/reader035/viewer/2022070411/568147c0550346895db501f6/html5/thumbnails/14.jpg)
Kerstin WolfAG GeomathematikTU Kaiserslautern
GRACE Science Team Meeting 2007:Joined International Symposium:GFZ-Potsdam, 15/-17/10/2007
Maximum of the absolute values of the 1st hybrid wavelet coefficients ( ) based on a time series of 47 GRACE-data sets (Feb. 03 – Dec. 06) computed with CuP-wavelet in time and space
Scale 3
Scale 6Scale 5
Scale 4
2. Time-Space Analysis
![Page 15: Multiscale Filter Methods Applied to GRACE and Hydrological Data](https://reader035.vdocuments.us/reader035/viewer/2022070411/568147c0550346895db501f6/html5/thumbnails/15.jpg)
Kerstin WolfAG GeomathematikTU Kaiserslautern
GRACE Science Team Meeting 2007:Joined International Symposium:GFZ-Potsdam, 15/-17/10/2007
Time dependent courses of the 2nd hybrid wavelet coefficients ( ) based on GRACE data (Feb. 03 – Dec. 06) with CuP-wavelet in time and space
Lilongwe(13°S 33°O)
Kaiserslautern(49°N 7°O)
2. Time-Space Analysis
Manaus(3°S 60°W)
Dacca(23°N 90°O)
![Page 16: Multiscale Filter Methods Applied to GRACE and Hydrological Data](https://reader035.vdocuments.us/reader035/viewer/2022070411/568147c0550346895db501f6/html5/thumbnails/16.jpg)
Kerstin WolfAG GeomathematikTU Kaiserslautern
GRACE Science Team Meeting 2007:Joined International Symposium:GFZ-Potsdam, 15/-17/10/2007
Overview
1. Motivation
2. Time-Space Analysis Using Tensor Product Wavelets
3. Comparison of GRACE and Hydrological Models (WGHM, H96, LaD)
4. Outlook
![Page 17: Multiscale Filter Methods Applied to GRACE and Hydrological Data](https://reader035.vdocuments.us/reader035/viewer/2022070411/568147c0550346895db501f6/html5/thumbnails/17.jpg)
Kerstin WolfAG GeomathematikTU Kaiserslautern
GRACE Science Team Meeting 2007:Joined International Symposium:GFZ-Potsdam, 15/-17/10/2007
3. ComparisonGRACE - Hydrological Models
Maximum of the absolute values of the pure wavelet coefficients ( ) computed out of a time series (Feb. 03 – Dec. 06) with CuP-wavelet in time and space at scale 4
GRACE
H96
WGHM
LaD
![Page 18: Multiscale Filter Methods Applied to GRACE and Hydrological Data](https://reader035.vdocuments.us/reader035/viewer/2022070411/568147c0550346895db501f6/html5/thumbnails/18.jpg)
Kerstin WolfAG GeomathematikTU Kaiserslautern
GRACE Science Team Meeting 2007:Joined International Symposium:GFZ-Potsdam, 15/-17/10/2007
3. ComparisonGRACE - Hydrological Models
GRACE-WGHM (corr = 0.79) GRACE-H96 (corr = 0.74)
GRACE-LaD (corr = 0.75)
Local correlation of the pure detail parts calculated with CuP-wavelet ( ) at scale 4 in time and space.In brackets: global correlation coefficient computed on the continents.
![Page 19: Multiscale Filter Methods Applied to GRACE and Hydrological Data](https://reader035.vdocuments.us/reader035/viewer/2022070411/568147c0550346895db501f6/html5/thumbnails/19.jpg)
Kerstin WolfAG GeomathematikTU Kaiserslautern
GRACE Science Team Meeting 2007:Joined International Symposium:GFZ-Potsdam, 15/-17/10/2007
3. ComparisonGRACE - Hydrological Models
Time dependent courses of the pure detail parts calculated with CuP-wavelet ( ) at scale 4 in time and space.
oo
bad correlation
good correlation
![Page 20: Multiscale Filter Methods Applied to GRACE and Hydrological Data](https://reader035.vdocuments.us/reader035/viewer/2022070411/568147c0550346895db501f6/html5/thumbnails/20.jpg)
Kerstin WolfAG GeomathematikTU Kaiserslautern
GRACE Science Team Meeting 2007:Joined International Symposium:GFZ-Potsdam, 15/-17/10/2007
3. ComparisonGRACE - Hydrological Models
Global correlation coefficients calculated using the pure wavelet coefficients ( ) on the continents
![Page 21: Multiscale Filter Methods Applied to GRACE and Hydrological Data](https://reader035.vdocuments.us/reader035/viewer/2022070411/568147c0550346895db501f6/html5/thumbnails/21.jpg)
Kerstin WolfAG GeomathematikTU Kaiserslautern
GRACE Science Team Meeting 2007:Joined International Symposium:GFZ-Potsdam, 15/-17/10/2007
1) Further analysis with different (band- / non-bandlimited) wavelets in the time and space domain:
2) Further analysis for the comparison of the hydrological models and the GRACE data:
• shannon wavelet, Abel-Poisson wavelet, Gauß-Weierstraß wavelet,…
• local calculations for regions of great accuracy (e.g. the Mississippi delta)
Aim:
to state an ‘ideal’ reconstruction of the signal in view of extraction of the hydrological model from the GRACE data
4. Outlook
![Page 22: Multiscale Filter Methods Applied to GRACE and Hydrological Data](https://reader035.vdocuments.us/reader035/viewer/2022070411/568147c0550346895db501f6/html5/thumbnails/22.jpg)
Kerstin WolfAG GeomathematikTU Kaiserslautern
GRACE Science Team Meeting 2007:Joined International Symposium:GFZ-Potsdam, 15/-17/10/2007
Thank you
for your attention!