Space and Time Multiscale Analysis System A sequential data assimilation approach

1. Space and Time Multiscale Analysis SystemA sequential data assimilation approach Yuanfu Xie, Steven Koch, Steve Albers Huiling Yuan and Brad Beechler Global Systems Division Earth System Research Laboratory

2. Resolvable Information for a Given Observation Network Obse r vation Longer wave Obse r vation Longer wave B ac k g r ound B ac k g r ound Difference on longer wave Difference on shorter wave

3. STMAS STMAS is implemented in two steps. • It retrieves the resolvable observation information. • After the resolvable information retrieved, STMAS is reduced to a standard statistical variational analysis With long waves retrieved, STMAS deals with a localized error covariance, a banded matrix.

4. Multigrid Technique Using the number of gridpoints to control the base functions.

5. An idealized multiscale case Left: Mesonet surface stations; Right: An analysis function

6. An idealized multiscale case (cont.)

7. A single 3DVAR with different α 0.9 0.7 α=0.5 These analyses tend to approximate the truth:

8. Different Implementations of STMAS Recursive filter Wavelet Multigrid

9. FAA/MIT Boundary Detection Application

10. STMAS for frontal boundary detection

11. STMAS vs. HPC