1. Dieter Mayer, Reinhold Steinacker, Andrea Steiner University of Vienna, Department of Meteorology and Geophysics, Vienna, Austria Presentation at the 10th European Conference on Applications of Meteorology (ECAM) Berlin, 14 September 2011

2. Outline 10th European Conference on Applications of Meteorology (ECAM) Berlin, 12-16 September 2011 IMG Vienna Mayer et.al. Motivation for VERA-QC Applicability and basis of VERA-QC Mathematical background of VERA-QC Deviations and error detection Handling special station alignments Conclusion and availability of VERA-QC

3. 10th European Conference on Applications of Meteorology (ECAM) Berlin, 12-16 September 2011 IMG Vienna Mayer et.al. Motivation for VERA-QC High quality data is needed as input for VERA What is VERA? Analysing observations to grid points (complex topography) Combining interpolation (TPS) & downscaling (Fingerprints) Features of VERA Model independent No need for first guess fields Works on real time & operational basis Applications of VERA & VERA-QC Real time model verification Basis for nowcasting Evaluation of case & field studies Computation of analysis ensembles High quality data is needed as input for VERA What is VERA? Analysing observations to grid points (complex topography) Combining interpolation (TPS) & downscaling (Fingerprints) Features of VERA Model independent No need for first guess fields Works on real time & operational basis Applications of VERA & VERA-QC Real time model verification Basis for nowcasting Evaluation of case & field studies Computation of analysis ensembles

4. 10th European Conference on Applications of Meteorology (ECAM) Berlin, 12-16 September 2011 IMG Vienna Mayer et.al. Selecting or designing a QC? Properties of VERA & its applications Existing QC- methods Requirements to select / design QC Bayesian QC Variational QC QC using OI QC using ID QC using SR Limit checks Internal consistency checks model independent no back- ground fields model verification real time fast (not iterative) field studies no statistical information complex topography handle inhomogeneous station distribution analysis ensembles propose deviations Answer: there is a need for a new QC-method

5. 10th European Conference on Applications of Meteorology (ECAM) Berlin, 12-16 September 2011 IMG Vienna Mayer et.al. Applicability of VERA-QC Basis: spatio and / or temporal consistency of data Requirement: High degree of redundancy in observations Example: VERA-Analysis for precipitation (green) & MSL-pressure (black) Dots and stars: Observations for precip. & pressure – Depending on station density & scale of phenomenon – Expressed as station distance and decorrelation length – QC applicable if / >> 1 (GTS: p MSL, ,  e )

6. 10th European Conference on Applications of Meteorology (ECAM) Berlin, 12-16 September 2011 IMG Vienna Mayer et.al. Basis of VERA-QC Error affected observations  (rough) observation field  o Corrected observations  (smoother) analysis field  a =  o +  Main task is to receive deviations  Example: South-West to North East pressure-gradient with some artificial errors: Note:  is not a simple difference between observation and interpolation

7. 10th European Conference on Applications of Meteorology (ECAM) Berlin, 12-16 September 2011 IMG Vienna Mayer et.al. Mathematical Core of VERA-QC Goal: receive deviations to obtain smooth analysis field. d1,d2, D: dimensions n, N: grid points P: prim. neighbors m,M: main stations s,S: second. neighbors - Defining cost function J as squared curvature of analysis field: - Curvature of analysis field C  a is not known  Taylor series expansion: - Building global cost function: (taking into account all stations and grid points) - Solving optimization problem for deviations :

8. Questions regarding the cost function: – Q1: Where should the cost function be evaluated? A1: Regular grid is too expensive, take station points – Q2: What are main stations, primary and secondary neighbors? A2: m: Main station: one station after another s: (secondary) neighbors of m p: (primary) direct neighbors of m – Q3: ? Which stations contribute to the Taylor series expansion? A3: A certain station and its natural neighbors.  More than one station is allowed to be erroneous! Concept of natural neighbors Method connecting stations: Delaunay Triangulation 10th European Conference on Applications of Meteorology (ECAM) Berlin, 12-16 September 2011 IMG Vienna Mayer et.al.

9. 10th European Conference on Applications of Meteorology (ECAM) Berlin, 12-16 September 2011 IMG Vienna Mayer et.al. Triangulation / Computing curvatures Typical example for realistic station distribution and Delaunay Triangulation Defining local grids around stations Interpolate station values  S to grid points n: Computing curvatures (Inverse distance interpolation)

10. Simplest example: 1D, 1 spike Outlier corrected partially, but counter swinging at neighbors Solution: correcting erroneous observation should reduce cost function. Compute weighted deviations : with 10th European Conference on Applications of Meteorology (ECAM) Berlin, 12-16 September 2011 IMG Vienna Mayer et.al. Weighting Deviations

11. Three possibilities to handle an observation 10th European Conference on Applications of Meteorology (ECAM) Berlin, 12-16 September 2011 IMG Vienna Mayer et.al. Deviations and Gross Errors No gross error Obs. corrected Gross error Obs. rejected No gross error Obs. accepted yes no yes no yes no a, b and c: parameter dependent, user defined thresholds VERA-QC is repeated without rejected observations

12. Error propagation possible at close by stations Example: circles with stations, cluster in center Both stations obtain significant deviations Combine both stations to one fictive cluster station Compute deviation for cluster station Add deviation to both stations Repeat VERA-QC for modified observations 10th European Conference on Applications of Meteorology (ECAM) Berlin, 12-16 September 2011 IMG Vienna Mayer et.al. Cluster Treatment

13. Properties of VERA-QC: – Applicable to 1, 2, 3 and 4 dimensional problems – High efficiency in detecting errors compared to other QC methods – No simple averaging algorithm – Can handle very inhomogeneous station distributions – Model independent, fast, no iterations necessary – Deviations can be stored to compute bias – Implemented as Matlab stand alone application, runs on Server & PC 10th European Conference on Applications of Meteorology (ECAM) Berlin, 12-16 September 2011 IMG Vienna Mayer et.al. Conclusions Further Informations: – Publication: Steinacker, R., D. Mayer, and A. Steiner 2011, Data Quality Control Based on Self Consistensy. Accepted in Monthly Weather Review. – Poster Presentation: A. Steiner, Operational Application of VERA-QC, Challenges and how to cope with them. Poster Hall, Thursday 16-17:00.

14. 10th European Conference on Applications of Meteorology (ECAM) Berlin, 12-16 September 2011 IMG Vienna Mayer et.al. Availability of VERA-QC Homepage: http://www.univie.ac.at/amk/veraflex/test/intern/ VERA-QC is freely available for non-commercial use

15. The End Acknowledgments: Austrian Science Fund (FWF), support under grant number P19658 Contact: dieter.mayer@univie.ac.at http://www.univie.ac.at/amk/veraflex/test/intern/ Thank you for your attention

16. Is VERA-QC an averaging technique? Considering a signal at only 3 stations (unlikely to be a gross error) Unweighted deviations smooth signal Weighted deviations only soften contrast 10th European Conference on Applications of Meteorology (ECAM) Berlin, 12-16 September 2011 IMG Vienna Mayer et.al.

17. VERA-QC in higher dimensions 10th European Conference on Applications of Meteorology (ECAM) Berlin, 12-16 September 2011 IMG Vienna Mayer et.al.

18. Interpolate irregularly distributed station values to regular grid (Thin plate spline) Downscaling with the help of idealized physically motivated patterns VERA in a nut shell 10th European Conference on Applications of Meteorology (ECAM) Berlin, 12-16 September 2011 IMG Vienna Mayer et.al. Solution Unexplained fieldExplained fieldWeight Fingerprint