Multiscale Filter Methods Applied to GRACE and Hydrological Data

Transcription

1 Multiscale Filter Methods Applied to GRACE and Hydrological Data Willi Freeden, Helga Nutz,

2 Overview 1. Motivation 2. Time-Space Analysis Using Tensor Product Wavelets 3. Comparison of GRACE and Hydrological Models (WGHM, H96, LaD) 4. Outlook

3 Overview 1. Motivation 2. Time-Space Analysis Using Tensor Product Wavelets 3. Comparison of GRACE and Hydrological Models (WGHM, H96, LaD) 4. Outlook

4 1. Motivation Time Series of Satellite Data (GRACE) Comparison Time Series of Hydrological Models (WGHM, H96, LaD) Comparative Analysis in Time and Space Domain All results are computed with data provided from GFZ-Potsdam (1.3)

5 1. Motivation Realization of a Time-Space Multiscale Analysis by use of Tensor Product Wavelets Raw Data: Time Series of Spherical Harmonic Coefficients Time Series of Water Columns Tensor Wavelet Analysis Based on Legendre Wavelets in the Time Domain and Spherical Wavelets in the Space Domain Determination of Temporally and Spatially Local Changes Pure and Hybrid Parts

6 1. Motivation Realization of a Time-Space Multiscale Analysis by use of Tensor Product Wavelets Raw Data: Time Series of Spherical Harmonic Coefficients Time Series of Water Columns Tensor Wavelet Analysis Based on Legendre Wavelets in the Time Domain and Spherical Wavelets in the Space Domain Determination of Temporally and Spatially Local Changes Pure and Hybrid Parts Why do we apply wavelets?

7 1. Motivation Uncertainty Principle (in space domain): Spherical Harmonics Ideal localization in the frequency domain But: Not any localization in the space domain Dirac- Function Ideal localization in the space domain But: Not any localization in the frequency domain

8 1. Motivation Uncertainty Principle (in space domain): Spherical Harmonics Ideal localization in the frequency domain But: Not any localization in the space domain - + Solution: Wavelets (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 Dirac- Function Ideal localization in the space domain But: Not any localization in the frequency domain

9 Overview 1. Motivation 2. Time-Space Analysis Using Tensor Product Wavelets 3. Comparison of GRACE and Hydrological Models (WGHM, H96, LaD) 4. Outlook

10 2. Time-Space Analysis Filter: Scaling Function Signal F Filter Method: Multiscale Analysis Smoothed Part Details Filter: Wavelets

11 2. Time-Space Analysis Why do we distinguish four parts? connection of temporal and spatial filters via a tensor product: Multiscale Analysis in Time Multiscale Analysis in Space smoothing detail smoothing detail smoothing in time and space pure detail in time and space smoothing in time detail in space hybrid detail in time smoothing in space

12 2. Time-Space Analysis Graphical Representation of a Multiscale Analysis Smoothed Parts Original Signal F Detailed Parts st Hybrid 2nd Hybrid Pure the higher the scale the finer the details

13 2. Time-Space Analysis Example of a Wavelet Filter: CuP-Wavelet (cubic polynomial) (filter for the detailed information) Waveletsymbol f. scales 2-5 Wavelet f. scales 2-5

14 2. Time-Space Analysis 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 CuPwavelet in time and space Scale 3 Scale 4 Scale 5 Scale 6

15 Time dependent courses of the 2nd hybrid wavelet coefficients ( ) based on GRACE data (Feb. 03 Dec. 06) with CuP-wavelet in time and space Manaus (3 S 60 W) 2. Time-Space Analysis Lilongwe (13 S 33 O) Dacca (23 N 90 O) Kaiserslautern (49 N 7 O)

16 Overview 1. Motivation 2. Time-Space Analysis Using Tensor Product Wavelets 3. Comparison of GRACE and Hydrological Models (WGHM, H96, LaD) 4. Outlook

17 3. Comparison GRACE - 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 WGHM H96 LaD

18 3. Comparison GRACE - 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 CuPwavelet ( ) at scale 4 in time and space. In brackets: global correlation coefficient computed on the continents.

19 3. Comparison GRACE - Hydrological Models o o bad correlation good correlation Time dependent courses of the pure detail parts calculated with CuP-wavelet ( ) at scale 4 in time and space.

20 3. Comparison GRACE - Hydrological Models Global correlation coefficients calculated using the pure wavelet coefficients ( ) on the continents

21 4. Outlook 1) Further analysis with different (band- / non-bandlimited) wavelets in the time and space domain: shannon wavelet, Abel-Poisson wavelet, Gauß-Weierstraß wavelet, 2) Further analysis for the comparison of the hydrological models and the GRACE data: 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

22 Thank you for your attention!